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In this paper, we defined subclasses of p-valent meromorphic functions defined by using integral operator. We investigate several interesting subordination properties for this subclasses of multivalent meromorphic functions. Relevant connections of the results which are presented in this paper with various known results are also considered. Keywords: Multivalent meromorphic functions, differential subordination, linear operator., 1 Introduction Let [[SIGMA].sub.p,n] denote the class of multivalent meromorphic functions of the form: [mathematical expression not reproducible] (1) which are analytic in the punctured unit disk U* = {z [...]

A bi-univalent function is a univalent function defined on the unit disk for which the inverse function has a univalent extension to the unit disk. The paper of H. M. Srivastava, A. K. Mishra and P. Gochhayat [Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), no. 10, 1188-1192] renewed the investigation of the estimate on initial coefficients of bi-univalent functions. In this paper, estimates for the initial coefficients of bi-univalent functions belonging to certain classes defined by subordination and of functions for which f and [f.sup.-1] belong to different subclasses of univalent functions are derived. Improvement of the earlier known estimates were also pointed out. Keywords and Phrases: Univalent functions, Bi-univalent functions, Coefficient estimate, Subordination., 1. Introduction Let A be the class of analytic functions defined on the open unit disk D: = {z [member of] C : [absolute value of z] < 1} and [...]

In this paper, we establish the Hyers-Ulam stability of the orthogonal quadratic functional equation of Pexiderized type f (x + y) + f (x - y) = 2g(x) + 2h(y), x [perpendicular to] y in which [perpendicular to] is the orthogonality in the sense of Ratz in modular spaces. Keywords and Phrases: Hyers-Ualm stability, Orthogonality,Orthogonally quadratic equation, Modular space., 1. Introduction The purpose of this paper is to prove the stability of orthogonal Pexiderized quadratic functional equation in the spirit of Hyers-Ulam in modular spaces. The theory of modulars [...]

Let R be a prime ring with center Z(R), right Utumi quotient ring U and extended centroid C, S be a non-empty subset of R and n [greater than or equal to] 1 a fixed integer. A mapping f: R [right arrow] R is said to be n-centralizing on S if [f (x), [x.sup.n]] [member of] Z(R), for all x [member of] S. In this paper we will prove that if F is a non-zero generalized derivation of R, I a non-zero left ideal of R, n [greater than or equal to] 1 a fixed integer such that F is n-centralizing on the set [I, I], then there exists a [member of] U and [delta] [member of] C such that F (x) = xa, for all x [member of] R and I(a - [delta]) = (0), unless when [x.sub.1][s.sub.4]([x.sub.2], [x.sub.3], [x.sub.4], [x.sub.5]) is an identity for I. Keywords and Phrases: Prime ring, Generalized derivation., Throughout the paper unless specifically stated, R always denotes a prime ring with center Z(R) and extended centroid C, right Utumi quotient ring U. For any pair of elements x, [...]

Given a sigraph S and a positive integer t, the t-path sigraph [(S).sub.t] of S is formed by taking a copy of the vertex set V (S) of S, joining two vertices u and v in the copy by a single edge e = u-v whenever there is a u - v path of length t in S and then by defining its sign to be - whenever in every u - v path of length t in S all the edges are negative. In this paper, we introduce a variation of the concept of t- path sigraphs studied above. The motivation stems naturally from one's mathematically inquisitiveness as to ask why not define the sign of an edge e = u-v in [(S).sub.t] as the product of the signs of the vertices u and v in S. It is shown that for any sigraph S, its t-path sigraph [(S).sub.t] is balanced. We then give structural characterization of t-path sigraphs. Further, in this paper we characterize sigraphs which are switching equivalent to their 2(3)-path sigraphs. Keywords and Phrases: Sigraphs, Balance, Switching, t-Path sigraphs, Negation of a sigraph., 1. Introduction For standard terminology and notion in graph theory we refer the reader to West (14); the non-standard will be given in this paper as and when required. We [...]

In this work, on the basis of homotopy analysis method, we propose a numerical procedure for solving multi-order fractional differential equations by transforming the original multi-order fractional differential equation into a system of single-order equations. To our knowledge this paper presents the first viable numerical method for an analytic solution of multi-order fractional differential equations. This approach provides a simple way to ensure the convergence of series of solution so that one can always get accurate enough approximations. Keywords and Phrases: Analytic solution, Multi-order fractional differential equations., 1. Introduction This paper concerns the numerical solution of multi-order fractional differential equations with general form [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where [D.sub.*.sup.α]y(t) is used to represent the Caputo-type [...]

The main objective of the present paper is to study some fundamental properties of solutions of certain Volterra type difference equations. A finite difference inequality with explicit estimate is used to establish the results. Keywords and Phrases: Qualitative properties, Volterra type difference equations, Finite difference inequality, Explicit estimate, Estimates on the solutions, Uniqueness and continuous dependence., 1. Introduction In this paper we consider the Volterra type difference equations of the form y(n)=f(n) + [n-1.summation over.s = 0] H(n, s, y(n), y(s)),(1.1) where y, f, H are [...]

We point out and correct some errors in a previous paper on two inequalities for random variables whose probability density functions are bounded. Keywords and Phrases: random variable, probability density function, Gruss inequality., 1. Introduction In a previous paper (4), Hwang using an improvement of Gruss inequality to establish some inequalities for expectation and the distribution function in order to improve the corresponding [...]

This paper deals with the development of an inventory model for non-instantaneous deteriorating items. This paper investigates an instantaneous replenishment inventory model for the above type of items under cost minimization, considering stock-dependent consumption rate under inflation and time discounting over a finite planning horizon. In the proposed model, shortages are allowed and partially backlogged. We also show that the total cost function is convex. To determine the optimal order quantity and the optimal interval of the total cost function, a solution algorithm is presented. Finally, the model is illustrated with the help of numerical examples. Sensitivity analysis of the optimal solution with respect to various parameters of the system is carried out and the results are discussed in detail. Keywords and Phrases: Inventory, Stock-dependent demand, Inflation, Partial backlogging, Non-instantaneous deterioration, Shortages., 1. Introduction It has been observed in supermarkets that the demand rate is usually influenced by the amount of the stock level, that is, the demand rate may go up [...]

There are three standard weight (distance) functions on a linear code viz. the Hamming weight (distance), the Lee weight (distance) and the Euclidean weight (distance). Plotkin (11) obtained an upper bound on the minimum weight (distance) of a code with respect to the Hamming weight (distance). A.D. Wyner and R.L. Graham (13) proved Plotkin's bound for Lee metric codes which was also conjectured by Lee (10). The first author also obtained another proof of Plotkin's bound with the Lee weight by a different approach (3). In this paper, we obtain Plotkin's bound for codes equipped with the Euclidean weight function. The Euclidean weight is useful in connection with the lattice constructions where the minimum norm of vectors in the lattice is related to the minimum Euclidean weight of the code (2). Using Plotkin's bound, we obtain a bound on the number of parity check digits required to achieve the minimum Euclidean square distance at least [d.sup.2] in a linear code. We also make a comparative study of the bounds for the Euclidean codes obtained in this paper with the corresponding bounds for the Hamming and Lee weight codes. Keywords and Phrases: Plotkin's bound, Linear code, Euclidean weight., 1. Introduction The minimum distance between any pair of code words in a code cannot exceed the average distance between all pairs of different code words. Using this observation, Plotkin [...]

In this paper the generalized Hyers-Ulam stability is proved for the following functional equation [4.summation over (i = 0)][.sub.4][C.sub.i][(-1)].sup.4-i]f(ix + y) = 0 following the spirit of the approach that was introduced in the paper of Th.M. Rassias, On, the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc, 72(1978), 297-300. Also, I investigate the superstability of the functional equation. Keywords and Phrases: Stability, Superstability, Generalized polynomial function of degree 3., 1. Introduction Throughout this paper, let V be a vector space and Y a Banach space. Let n be a positive integer. For a given mapping f : V → [...]

In this paper, the (ψ, γ)--stability of the quadratic functional equa- tion is considered on arbitrary groups. It is proved that every group can be embedded into a group in which the quadratic equation is (ψ, γ)-stable. Further, it is shown that the quadratic functional equation is (ψ, γ)-stable on all abelian groups and some non-abelian groups such as UT(3, K), T(3, K) and T(2, K), where K is an arbitrary field. The results of Skof (19) and Czerwik (4) are generalized in this paper. Keywords and Phrases: (ψ, γ)-pseudoquadratic map, (ψ, γ)-quasiquadratic map, Quadratic map, Quadratic functional equation, Semidirect product of groups, (ψ, γ)-stability of quadratic functional equation, Wreath product of groups., 1. Introduction In 1940 to the audience of the Mathematics Club of the University of Wisconsin S. M. Ulam presented a list of unsolved problems (20). One of these problems [...]

In this paper we establish Hyers--Ulam--Rassias stability of the following quadratic mapping of Apollonius type Q(z - x) + Q(z - y) = 1/2Q(x - y) + 2Q(z - [x + y]/2) (1) in non-Archimedean spaces. The term Hyers--Ulam--Rassias stability is due to the seminal paper: Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297-300. Keywords and Phrases: Apollonius' identity, Hyers--Ulam--Rassias stability, Quadratic function, Quadratic functional equation of Apollonius type., 1. Introduction The stability problem of functional equations originated from a question of S.M. Ulam (25) concerning the stability of group homomorphisms: Let [G.sub.1] be a group and let [G.sub.2] [...]

The object of the present paper is to generalize the Srivastava--Buschman's solution of the Convolution Integral Equation involving the Fox H-function kernel to the case of Generalized H-function kernel. There are some novel functions that form special cases of the generalized H-function but not Fox H-function. In the present paper, we shall give the solution of convolution equations involving two of such novel functions as kernels. Keywords and Phrases: Convolution integral equation, Generalized H-function (The [bar.H]-function), Laplace transform., 1. Introduction Srivastava and Buschman established the following theorem giving the solution of the Convolution integral equation whose kernel is Fox H-function. Theorem 1 (Srivastava and Buschman (5),(6)). The convolution [...]

In the retail business, an additional storage (warehouse) is very essential to reduce the lost sale. Particularly, when the area of the existing storage (Owned warehouse, OW) in an important market place (like, super market, corporation market etc.) is relatively small, the need of the additional storage can be released. In this paper, a single item inventory model is developed considering two separate storage facilities (owned warehouse, OW and rented warehouse, RW) due to insufficient space of existing warehouse. The stocks of additional storage RW are transferred to OW in bulk release pattern and the associated transportation cost is taken into account. Here, we consider the effect of different stock-dependency and marketing policies such as the price variation and the frequency of advertisement on the selling rate of an item. Shortages are not allowed. To replenish the item to the storage/warehouse, transportation cost is considered explicitly. In most situations, this cost is assumed to be fixed and are, therefore, included in the ordering cost or variable and included in the cost of the item. Here, it is assumed that this transportation cost is depended on the lot-size as well as the distance between the source and the destination. Different cases of the system have been mentioned and developed. A numerical example is given to illustrate the solution procedure of the model. Finally, based on this example, a sensitivity analysis is done for the effect of different parameters on the optimal profit and cycle length. Scope and purpose The existing two storage models were developed based on the assumption that storage capacity of the rented warehouse (RW) is unlimited. Obviously, this is an unrealistic assumption as the capacity of storage is always limited. In this paper, a two storage inventory model with frequency of advertisement, selling price and stock-dependent selling rate is developed considering limited storage capacity of the rented warehouse. This model is solved by a gradient method based mathematical program. This methodology of model development and its solution are quite general and it can be applied to inventory models of any item whose selling rate is dependent on stock-level and marketing decisions. The purpose of this paper is to report an economic replenishment policy in which decision-makers can know when and how much amount to replenish as well as which system to choose for storing the replenished items. Keywords and Phrases: Stock-dependent selling rate, Inventory, Two storage, Transportation, Bulk released pattern., 1. Introduction Now-a-days, an item is well known to the people in the modern society through advertisement in the well-known media like, Newspaper, Magazine, Radio, TV, Cinema etc. and also [...]

In this paper we show that Hyers-Ulam-Rassias stability holds for Pexiderized additive functional equations in the framework of intuitionistic fuzzy Banach spaces. We consider a two-variable pexiderized additive functional equation. The approach to the present stability problem is through fixed point method for which we apply the Banach contraction mapping principle in generalized metric spaces which is a structure where infinite distances are admissible. Keywords: Hyers-Ulam stability; Pexider type functional equation; intuitionistic fuzzy normed spaces; alternative fixed point theorem., 1 Introduction In Mathematics, functional equation are studied in various contexts. In particular the study on the stabilities of functional equation has a large literature. It started with the basic [...]

The exponentiated Pareto type I distribution is used as a model for the distribution of city populations within a given area. In this paper, we have considered the dual generalized order statistics from this distribution. We obtained exact explicit expressions as well as recurrence relations for single and product moments of dual generalized order statistics from generalized Pareto distribution. Then, we use these results, we have tabulated the first four moments, skewness and kurtosis of order statistics from samples of sizes up to 10 for various values of the parameters. Keywords: Sample; dual generalized order statistics; record values; single and product moments; recurrence relations; exponentiated Pareto type I distribution., 1 Introduction The Pareto distribution was first proposed as a model for the distribution of incomes. It is also used as a model for the distribution of city populations within [...]

In the present paper we established the relations between growth parameters order and type in terms of coefficients occurring in generalized Faber series expansions of entire function and corresponding best linear approximation errors in supnorm in doubly connected domains. Keywords: Generalized Faber series, best linear approximation errors, order and type, doubly connected domains and entire functions., 1 Introduction Let K be a continuum (not a point) on the complex plane C that does not separate the plane and let [OMEGA] be an arbitrary domain containing K [...]

Let B(H) be the C(*)-algebra of all bounded linear operators on Hilbert space H. In this paper, we introduce three concept of (*)-products on B(H), and present a form for a unital surjective bounded linear map [phi]: B(H) [right arrow] B(H), which preserves these (*)-products in both directions. Key words and phrases. Hilbert space; (*)-product; preserving linear map; C(*)-algebra., 1. INTRODUCTION AND PRELIMINARIES Suppose that X and Y are linear spaces and [phi]: X [right arrow] Y is a map. We say that [phi] is a preserving map in [...]

In this paper, basic notions of von Neumann algebra and its direct analogous in the realm of groupoids and measure spaces have been considered. By recovering the action of a locally compact Lie group from a crossed product of a von Neumann algebra, other proof of one of a geometric proposition of O'Neil and an extension of it has been proposed. Also, using the advanced exploration of nilmanifolds in measure spaces and their corresponding automorphisms (Lie algebraic derivations) a different proof of an analytic proposition of Gordon and Mao has been attained. These two propositions are of the most important ones for rigidity problems of Riemannian manifolds especially 2-step nilmanifolds. Keywords. Von Neumann algebras, 2-step nilmanifolds, Free and ergodic actions, Derivations, Automorphisms., 1. Introduction Motivation. Let M is a simply connected 2-step nilpotent Lie group with a left invariant metric and [LAMBDA] is a cocompact discrete subgroup of isometries of M. In [...]

In this paper, a link between general topological space and soft topological space is identified using the parameterized family of topologies induced by the soft topology. The concept of quasi soft set is introduced to characterize certain soft topological concepts using the parameterized family of topologies induced by the soft topology. KEYWORDS: Soft sets, Soft topology, Soft [T.sub.i], Soft regular, Soft normal., 1 Introduction Molodstov[8] originate soft sets for dealing with uncertainities in many practical problems in science and Engineering. Maji et.al. [7],[6] studied the theoretical concepts of soft sets and applied [...]

In this paper, the concept of [[omega].sub.[theta]]-continuous function from an arbitrary topological space into the product space will be characterized. Moreover, some versions of separation axioms with respect to [[omega].sub.[theta]]-open set will be introduced and characterized. Keywords: [[omega].sub.[theta]]-continuous, [[omega].sub.[theta]]-Hausdorff, [[omega].sub.[theta]]-regular, [[omega].sub.[theta]]-normal, 1 Introduction The first attempt to replace various concepts in topology with concepts possessing either of weaker or stronger properties was done by N. Levine [4] in 1963. In his [...]

Using the principle of subordination, in the present paper we obtain the sharp subordination and superordination-preserving properties of some convex combinations associated with a linear operator in the open unit disk. The sandwich-type theorem on the space of meromophic functions for these operators is also given, together with a few interesting special cases obtained for an appropriate choices of the parameters and the corresponding functions., 1. INTRODUCTION Let denote by H(U) the space of all analytical functions in the unit disk U = {z [member of] C: |z| < 1}, and for a [member of] [...]

A new differential operator [mathematical expression not reproducible] is introduced for functions of the form [mathematical expression not reproducible] which are meromorphic in the punctured unit disc U*:= {z [member of] C: 0 < |z| < 1}. We introduce the class [mathematical expression not reproducible] of meromorphically functions that generalize and extend many classes previously studied by different authors, and the main object of this paper is to investigate various important properties and characteristics for this class. In addition, we proved that a special property is preserved by some integral operators., 1. INTRODUCTION Let [[SIGMA].sub.p,n,] with n [greater than or equal to] 1 - p, denote the class of functions of the form (1.1) [mathematical expression not reproducible] which are analytic [...]

In this paper, we study the boundedness and asymptotic behavior of fuzzy nonlinear difference equation of the form [mathematical expression not reproducible] where [A.sub.i], [B.sub.i] i [member of] {0,1, x x x, k}, are the positive fuzzy numbers, [p.sub.i], i [member of] {0,1, x x x, k} are positive constants and [x.sub.i] i [member of] {0, -1, x x x, -k, -k + 1} are positive fuzzy numbers. Keywords: Fuzzy Difference Equations, Nonlinear, Boundedness, Fuzzy number, [alpha]-cuts, 1 Introduction Fuzzy difference equation is a difference equation where constants and the initial values are fuzzy numbers and its solutions are sequence of fuzzy numbers. Fuzzy difference equations are [...]

Find an approximate solution is one of the most important problems in our days, in this paper we look for an approximate solution for Volterra nonlinear integral equation using a combination between Newton-Kantorovich method and adapted trapezoidal method. Then we do a comparaison between the numerical results obtained by this method against ones obtained by another authors. KEYWORDS AND PHRASES. Nonlinear Volterra integral equation, Newton-Kantorovich method, adapted trapezoidal method, 1. INTRODUCTION Integral equations is a very useful mathematical tools in both pure and applied mathematics, appears in various fields of science and numerous applications such that elasticity, plasticity, heat [...]

The objective of this paper is to obtain best possible upper bounds for the second and third Hankel functionals associated with the [k.sup.th] root transform [[f([z.sup.k])].sup.1/k] of normalized analytic function f(z) when it belongs to it belongs to bounded turning functions, defined on the open unit disc in the complex plane, using Toeplitz determinants. Keywords and phrases: Bounded turning function, upper bound, second and third Hankel functional, positive real function, Toeplitz determinants., 1 Introduction Let A denote the class of all functions f(z) of the form f(z) = z + [[infinity].summation over (n=2)] [a.sub.n][z.sub.n] (1.1) in the open unit disc E = [...]

In this paper, we prove the strong convergence of an approximating common element of the set of fixed points of a nonexpansive multivalued mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping in a Hilbert space by using the modified extragradient method. As applications, we give the example and numerical results for supporting our main theorem. Keywords: Extragradient method; Variational inequality; Nonexpansive multi-valued mapping; Iteration; Hilbert space., 1 Introduction Let H be a real Hilbert space with inner product [??]*,* [??] and norm [parallel] * [parallel], respectively. Let C be a nonempty closed convex subset of H. [...]

In this paper, we establish the characterization of closed ideals of C(X) in terms of the topology on X. We also discuss an application of multiplicative linear functionals on C(X). Key words and phrases. Compactness, Hausdorff space, Characterization of Ideals., 1. INTRODUCTION AND PRELIMINARIES The space of all continuous functions C(X) has always inspired many mathematicians to extend their valuable research in the area of analysis. Vast literature is available [...]

For analytic functions f(z) normalized by f(0) = f'(0) - 1 = 0 in the open unit disk U, a class [A.sup.k]([[beta].sub.1], [[beta].sub.2], [[beta].sub.3], [[beta].sub.4]; [lambda]) of function f(z) defined by [mathematical expression not reproducible] where [D.sub.k] denote the Ruscheweyh differential operator of order k, k [member of] [N.sub.0]:= N [union] {0}, for some complex number numbers [[beta].sub.1], [[beta].sub.2], [[beta].sub.3], [[beta].sub.4] and for some real [lambda] > 0 is introduced. The object of the present paper is to obtain some interesting properties of function class [A.sup.k]([[beta].sub.1], [[beta].sub.2], [[beta].sub.3], [[beta].sub.4]; [lambda]). Our results generalize the results due to Uyanik et al. (2010) and Uyanik and Owa (2011). Key words and phrases. Analytic function, Univalent function, Ruscheweyh derivative., 1. INTRODUCTION AND MOTIVATION Let H(U) be the class of analytic functions in the open unit disk U:= {z [member of] C: |z| < 1} and H[a, n] be the [...]

Recently, the present authors have introduced the notion of generalized quasi-conformal curvature tensor which bridges Conformai curvature tensor, Concircular curvature tensor, Projective curvature tensor and Conharmonic curvature tensor. The object of the present paper is to find out curvature conditions for Ricci solitons to be shrinking or steady or expanding. Key Words:N (k)-contact metric manifold; quasi-conformal like curvature tensor; Ricci solitons Shrinking, Steady and Expanding., 1 Introduction Recently, in tune with Yano and Sawaki [24], the first two authors [19] have introduced and studied generalized quasi-conformal curvature tensor W in the context of N(k, [mu])-manifold. [...]

Let M be a W*-algebra and A [??] M a commutative W*-subalgebra of M containing the identity element of M. Let [sigma]: M [right arrow] M be a continuous homomorphism and [delta]: M [right arrow] M a [sigma]-derivation. In this paper, it is proved that there exists a [x.sub.0] [member of] M such that [delta]([alpha]) = [sigma]([alpha])[x.sub.0] - [x.sub.0][sigma](a), for each a [member of] A. Also, it is proved that if {[d.sub.n]} is a continuous strongly [sigma]-higher derivationon on M, then there exist [x.sub.1], [x.sub.2], [x.sub.3],...[x.sub.n] [member of] M such that [d.sub.n](a) = [[sigma].sup.n](a)[x.sub.n] - [x.sub.n][[sigma].sup.n](a) - [x.sub.n-1] [d.sub.1]([[sigma].sup.n-1](a)) - [x.sub.n-2][d.sub.2]([[sigma].sup.n-2])(a) -... - [x.sub.1][d.sub.n-1]([sigma](a)) for each a [member of] A. Key words and phrases. derivation, [sigma]-derivation, [sigma]-higher derivation, inner derivation, W*-algebra., 1. INTRODUCTION Let A be an algebra. We say that a linear mapping d on A is a derivation if it satisfies d(ab) = ad(b) + d(a)b ([for all]a, b [...]

The growing complexity of computational modelling and its applications demands the simplicity of mathematical equations and techniques for solving today's scientific problems and challenges. This paper presents a model of iterative computation that deals with design and optimization of recursive formulae related to series and summability with real-time function. Keywords: recursive algorithm, real-time system, iterative computation, Introduction Computational technique for solving the sequences and series problems along with its applications [1-6] plays a vital role in mathematical modelling. In this research article a model of iterative [...]

In the present paper we study characterizations of odd and even dimensional N(k)-mixed quasi-Einstein manifold and finally prove that a N(k)-mixed quasi-Einstein manifold is a semi mixed quasi-Einstein manifold under a certain condi-tion. Key words : N(k)-mixed quasi Einstein manifold, semi mixed-Einstein manifold., 1. Introduction A Riemannian manifold (M, g) with dimension (n [greater than or equal to] 2) is said to be an Einstein manifold if the Ricci tensor satisfies the condition [...]

In this paper, we first consider a non - selfadjoint differen-tial operator on Hilbert space Hl = [L.sup.2] [(0, 1).sup.l] with Dirichlet-type boundary conditions in form [mathematical expression not reproducible] Here, 0 [less than or equal to] [beta] < 1, t [member of] [0, 1] and the matrix function A(t) has distinct eigenvalues [[mu].sub.1](t),... , [mu]l(t) which are different from zero and located in the complex plane in veiw of [[PHI].sub.[??]], where [PHI][??] = {z [member of] C : |ar g z| < [??], [??] [member of] (0, [pi])}. Finally, we investigate some spec-tral properties of the degenerate non-selfadjoint elliptic differential operators P acting on Hl. In particular, we will determine the resolvent estimate of the operator P that satisfies Dirichlet-type boundary conditions in spaces [H.sub.1] and Hl., 1 Introduction Here, we need to recall the definition of the weighted Sobolev space. The symbol [mathematical expression not reproducible] (l -times) denotes the space of vector functions u(t) = [...]

The object of this paper is to study the sequence spaces : [DELTA]W(A, M,q,p,u,s), [DELTA][W.sub.0](A, M, [bar.q], p, u, s) and [DELTA][W.sub.[infinity]](A, M, [bar.q], p, u, s) associated with strongly Cezaro summable sequences and discuss some topological properties of these spaces and other related results., 1. DEFINITIONS AND NOTATIONS Let w denote the set of all sequences x = ([x.sub.n]), real or complex, let p = ([p.sub.n]),q = (qn) and [bar.q] = ([[bar.q].sub.n]) denote the [...]

Let G be an abelian group, C be the field of complex numbers, and 0 [not equal to] [alpha] [pounds sterling] G be a fixed element. In this paper, we determine the general solution f, g : G [right arrow] C of the functional equation f(x - y+[alpha]) + g(x+y+[alpha]) = 2 f(x) f(y) for all x, y [member of] G. Keywords and phrases. Abelian group, cosine functional equation, functional equation with restricted arguments, homomorphism., 1. INTRODUCTION Let R be the field of real numbers and C be the field of complex numbers. Let G be an abelian group and [alpha] be a fixed nonzero [...]

The present paper deals with the study of Riemannian mani-folds whose metric is Ricci almost soliton with a conformal Killing vector field. We also study Ricci almost solitons on Riemannian manifolds with respect to semi-symmetric metric connection and obtain a necessary and sufficient condition of a Ricci almost soliton on Riemannian manifold with respect to semi-symmetric metric connection to be Ricci almost soliton on Riemannian manifold with respect to Levi-Civita connection., 1. INTRODUCTION In 1982, Hamilton [10] introduced the notion of Ricci flow to find a canonical metric on a smooth manifold. Then Ricci flow has become a powerful tool for [...]

Abstract In this paper, we generalize two theorems on the uniqueness of non-linear differential polynomials sharing 1-points, which improves a result of Indrajit Lahiri and Pulak Sahoo[14]. Keywords and Phrases: [...]

Abstract In this paper, we have presented a family of fourth order iterative method and another family of sixth order iterative method without memory based on power mean using weight [...]

Abstract In this paper we study some applications of the theory of differential subordination defined on the space of univalent functions which are defined by linear operators. Also, some examples [...]

Abstract In this paper, we introduce the subclasses [M.sup.-1]([alpha]), [N.sup.-1]([alpha]), [(M*).sup.-1]([alpha]) and [(N*).sup.-1]([alpha]) of analytic functions of reciprocal order [alpha]. Coefficient inequalities and an interesting subordination results are obtained. Keywords [...]

Abstract The aim of this paper is to study super quasi-Einstein manifolds. Here, we prove some geometric and global properties of super quasi-Einstein manifolds. Moreover, we present an existence result [...]

Abstract In this paper, the general solutions of a sum form functional equation containing four unknown mappings have been obtained without imposing any regularity condition on any of the four [...]

Abstract In this paper we consider exponentiated inverted Weibull distribution. Exact expressions and some recurrence relations for single and product moments of lower generalized order statistics are derived. Further the [...]

The object of the present paper is to study weakly symmetric, weakly Ricci symmetric, generalized recurrent and generalized Ricci recurrent LP-Sasakian manifolds admitting a quarter symmetric non metric connection [nabla]. Keywords and Phrases: Quarter-symmetric non metric connection, LP-Sasakian manifolds, Weakly symmetric, Weakly Ricci symmetric, Generalized recurrent, Generalized Ricci recurrent., 1. Introduction The idea of metric connection with torsion tensor in a Riemannian manifold was introduced by Hayden [19]. Later, Yano [11] studied some properties of semi symmetric metric connection [...]

The main object of this present paper is to investigate the problem of majorization for certain classes of analytic functions of complex order associated associated with the Dziok-Srivastava and the SrivastavaWright convolution operators. Moreover we point out some new or known consequences of our main result. Keywords and Phrases: Analytic functions, Starlike and convex functions of complex order, Qusai-subordination, Majorization problems, Hadamard product (convolution), Dziok-Srivastava operator, Srivastava-Wright convolution operator., 1. Introduction Let S be the class of functions which are analytic in the open unit disk U = {z [member of] C : [absolute value of z] < 1} [...]

The object of the present paper is to study some classes of weakly projective symmetric manifolds [(WPS).sub.n]. At first some properties of the 1-forms of [(WPS).sub.n] (n > 2) have been studied. Next we consider conformally flat [(WPS).sub.n] (n > 2). Among others we obtain that, in a [(WPS).sub.n] the integral curves of the vector [[rho].sub.3] defined by (1.3), are geodesics under certain condition. Next we consider [(WPS).sub.4] perfect fluid spacetime. Finally, we give an example of a [(WPS).sub.n]. Keywords and Phrases: Weakly symmetric manifolds, Weakly projective symmetric manifolds., 1. Introduction As is well known, symmetric spaces play an important role in differential geometry. The study of Riemannian symmetric spaces was initiated in the late twenties by Cartan [3], [...]

The object of the present paper is to classify an LP-Sasakian manifold with a coefficient [alpha] satisfying certain curvature conditions. Also [xi]-concircularly flat and [phi]-concircularly flat LP-Sasakian manifold with a coefficient [alpha] have been studied. Finally, we have shown the applications of such a manifold in general relativity and cosmology. Keywords and Phrases: LP-Sasakian manifold with a coefficient [alpha], Einstein manifold, [eta]-Einstein manifold, Concircular curvature tensor, [xi[-concircularly flat, [phi]-concircularly flat., 1. Introduction In 1989, Matsumoto [11] introduced the notion of LP-Sasakian manifolds. Then Mihai and Rosca [8] introduced the same notion independently and they obtained several results in this manifold. [...]

Let R be a prime ring of characteristic not 2, U a nonzero square closed Lie ideal of R and F, G be two generalized derivations of R with associated derivations d and [delta] of R respectively. In the present paper, we study the situations (1) F(u)G(v) - uv [member of] Z(R), (2) F(u)G(v) + uv [member of] Z(R), (3) d(u)F(v) - vu [member of] Z(R), (4) d(u)F(v) + vu [member of] Z(R); for all u,v [member of] U and show that if d [not equal to] 0 and [delta] [not equal to] 0, then U [subset or equal to] Z(R). Keywords and Phrases: Prime ring, Lie ideal, Derivation, Generalized derivation., 1. Introduction Let R be a prime ring with center Z(R). For any pair of elements x,y [member of] R, we shall write [x,y] for the commutator xy - yx. [...]