Search

In this short paper, generally, we define a family of functions fk depends on the Eisenstein series with weight 2k, for k ( N. More detail, by considering the function fk, we define a derivative formula for generating weakly modular forms with weight 12. As a result for this, we claim that this formula gives an advantage to find the special solutions of some differential equations.

In this paper, we consider a class of generalized operator equilibrium problems and derive a Minty type lemma for this class of problems. Further, we establish some existence theorems for the generalized operator equilibrium problems. The theorems presented in this paper generalize and unify many well-known results in the literature.

In the paper under review, we analyze various types of degenerate abstract Volterra integrodifferential equations in sequentially complete locally convex spaces. From the theory of non-degenerate equations, it is well known that the class of (a,k)-regularized C-resolvent families provides an efficient tool for dealing with abstract Volterra integro-differential equations of scalar type. Following the approach of T.-J. Xiao and J. Liang [41]-[43], we introduce the class of degenerate exponentially equicontinuous (a,k)- regularized C-resolvent families and discuss its basic structural properties. In the final section of paper, we will look at generation of degenerate fractional resolvent operator families associated with abstract differential operators.

Inthispaper, weintroduceandstudythenotionofweightedslantHankeloperatorK β ϕ , ϕ ∈ L ∞ (β) on the space L 2 (β), β = {βn}n∈Z being a sequence of positive numbers with β0 = 1. In addition to some algebraic properties, the commutant and the compactness of these operators are discussed. 1. Preliminaries and Introduction Laurent operators (8) or multiplication operators Mϕ(f 7→ ϕf) on L 2 (T) induced by ϕ ∈ L ∞ (T), T being the unit circle, play a vital role in the theory of operators with their tendency of inducing various classes of operators. In the year 1911, O. Toeplitz (15) introduced the Toeplitz operators given as Tϕ = PMϕ, where P is an orthogonal projection of L 2 (T) onto H 2 (T) and later in 1964, Brown and Halmos (4) studied algebraic properties of these operators. We refer (1, 2, 4, 7, 9 and 12) for the applications and extensions of study to Hankel operators, slant Toeplitz operators, slant Hankel operators and k th -order slant Hankel operators. In the mean time, the notions of weighted sequence spaces H 2 (β) and L 2 (β) also gained momentum. Shield (14) made a systematic study of the Laurent operators on L 2 (β). We prefer to call the Laurent operator on L 2 (β) as weighted Laurent operator. Weighted Toeplitz operators, Slant weighted Toeplitz operators and weighted Hankel operaots on L 2 (β) are discussed in (10), (3) and (5, 6) respectively. In this paper, we extend the study to a new class of operators namely, weighted slant Hankel operators and describe its algebraic properties. We now begin with the notations and preliminaries that are needed in the paper. We consider the space L 2 (β) of all formal Laurent series f(z) = ∑ n∈Z a nz n , an ∈ C, (whether or not the series

Aiming at the study of the compression of Khalimsky topological spaces which is an interesting field in digital geometry and computer science, the present paper develops a new homotopy thinning suitable for the work. Since Khalimsky continuity of maps between Khalimsky topological spaces has some limitations of performing a discrete geometric transformation, the paper uses another continuity (see Definition 3.4) that can support the discrete geometric transformation and a homotopic thinning suitable for studying Khalimsky topological spaces. By using this homotopy, we can develop a new homotopic thinning for compressing the spaces and can write an algorithm for compressing 2D Khalimsky topological spaces.

In previous papers, various notions of (strongly) closed subobject, (strongly) open subobject, connected and Ti, i = 0, 1, 2 objects in a topological category were introduced and compared. The main objective of this paper is to characterize each of these classes of objects in the category of closure spaces as well as to examine how these generalizations are related. 2010 Mathematics Subject Classifications. 54B30, 54D10, 54A05, 54A20, 18B99, 18D15. .

Beer and Di Concilio [4] have given necessary and sufficient conditions for a two-sided Attouch-Wets topology to contain another on the hyperspace of non-empty closed subsets of a metrizable space as determined by metrics compatible with the topology. In the present paper, we characterize comparability of lower Attouch-Wets topologies as determined by compatible metrics.

In the present paper, we obtain some new results by applying well-known Jack?s lemma. Moreover, the second-order differential subordinations associated with convex functions are also considered.

In this paper, we introduce the notion of Saphar linear relation in a Banach space and we study the behaviour of such notion in polynomials.

The purpose of this paper is to present some fixed point results in b-metric spaces using a contractive condition of Hardy-Rogers type with respect to the functional H. The data dependence of the fixed point set, the well-posedness of the fixed point problem, as well as, the Ulam-Hyres stability are also studied.

In this paper, we introduce the notion of strict pseudo-contractive mappings in the framework of CAT(0) metric spaces. Some properties of such mappings including demiclosed principle are investigated. Also, strong convergence and ?-convergence of the well-known Mann iterative algorithm is established for strict pseudo-contractive mappings.

In this paper, some additive properties of the pseudo Drazin inverse are obtained in a Banach algebra. In addition, we find some new conditions under which the pseudo Drazin inverse of the sum a + b can be explicitly expressed in terms of a, az, b, bz. In particular, necessary and sufficient conditions for the existence as well as the expression for the pseudo Drazin inverse of the sum a+b are obtained under certain conditions. Also, a result of Wang and Chen [Pseudo Drazin inverses in associative rings and Banach algebras, LAA 437(2012) 1332-1345] is extended.

In this paper, we establish some fixed point theorems in G-metric spaces involving generalized cyclic contractions. Some subsequent results are derived. The presented results generalize many well known results in the literature. Moreover, we provide some concrete examples and an application on the existence and uniqueness of solutions to a class of nonlinear integral equations.

In this paper the n-tuples of commuting isometric semigroups on a Hilbert space and the product semigroup generated by them are considered. Properties of the right defect spaces and characterizations of the semigroups of type ?s? are given. Also, the Wold-type decompositions with 3n summands for n-tuples of commuting isometric semigroups are introduced. The existence and uniqueness of such decompositions are analysed and several connections with the Wold decompositions of each semigroup and their product semigroup are presented.

The main purpose of this paper is to introduce and investigate the concepts of lacunary strong summability of order and lacunary statistical convergence of order of real-valued functions which are measurable (in the Lebesgue sense) in the interval (1,∞). Some relations between lacunary statistical convergence of order and lacunary strong summability of order are also given.

The concept of a left n-inverse of a bounded linear operator on a complex Banach space was introduced recently. Previously, there have been results on products and tensor products of left n-inverses, and the representation of left n-inverses as the sum of left inverses and nilpotent operators was being discussed. In this paper, we give a spectral characterization of the left n-inverses of a finite (square) matrix. We also show that a left n-inverse of a matrix T is the sum of the inverse of T and two nilpotent matrices.

In the present paper, utilizing the techniques of suitable measures of noncompactness in Banach algebra, we prove an existence theorem for nonlinear functional-integral equation which contains as particular cases several integral and functional-integral equations that appear in many branches of nonlinear analysis and its applications. We employ the fixed point theorems such as Darbo?s theorem in Banach algebra concerning the estimate on the solutions. We also provide a nontrivial example that explains the generalizations and applications of our main result.

In [ Filomat, 28 (2014), 1537-1541], Bor proved a theorem dealing with absolute Riesz summability factors of infinite series. In this paper, we generalize that result for the absolute matrix summability factors of infinite series. Some new results are also obtained.

Abbas, Ali and Salvador [Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory Appl. 2013, 2013:243] extended the concept of F- contraction mapping introduced in [21], to two mappings. The aim of this paper is to introduce the notion of a generalized F1- weak contraction mapping and to study sufficient conditions for the existence of common fixed points for such class of mappings. As applications, related invariant approximation results are derived. The results obtained herein unify, generalize and complement various known results in the literature.

In this paper, we extend the definition of weakly second submodule of a module over a commutative ring to a module over an arbitrary ring. First, we investigate some properties of weakly second submodules. We define the notion of weakly second radical of a submodule and determine the weakly second radical of some modules. We also define the notion of weak m*-system and characterize the weakly second radical of a submodule in terms of weak m*-systems. Then we introduce and study a topology on the set of all weakly second submodules of a module. We give some results concerning irreducible subsets, irreducible components and compactness of this topological space. Finally, we investigate this topological space from the point of view of spectral spaces.

Aktu?lu and H. Gezer [Central European J. Math. 7 (2009), 558-567] introduced the concepts of lacunary equistatistical convergence, lacunary statistical pointwise convergence and lacunary statistical uniform convergence for sequences of functions. In this paper, we apply the notion of lacunary equistatistical convergence to prove a Korovkin type approximation theorem by using test functions 1, x/1-x,(x/1-x)2.

In this paper, we examine the stability of several spectral properties under commuting perturbations. In particular, we show that if T ( L(X) is an isoloid operator satisfying generalized Weyl?s theorem and if F ( L(X) is a power finite rank operator that commutes with T, then generalized Weyl?s theorem holds for T + F. In addition, we consider the permanence of Bishop?s property (?), at a point, under commuting perturbation that is an algebraic operator.

Let B be a C*-algebra, E be a Hilbert B module and L(E) be the set of adjointable operators on E. Let A be a non-zero C*-subalgebra of L(E). In this paper, some new kinds of irreducibilities of A acting on E are introduced, which are all the generalizations of those associated to Hilbert spaces. The difference between these irreducibilities are illustrated by a number of counterexamples. It is concluded that for a full Hilbert B-module, these irreducibilities are all equivalent if and only if the underlying C*-algebra B is isomorphic to the C*-algebra of all compact operators on a Hilbert space.

We originate some existence results on periodic and fixed point using generalized (???)- contractions and generalized (?,?)-contractive mappings with weaker Meir-Keeler function in the setup of a complete generalized metric space in sense of Branciari without Hausdorff assumption. Our results generalize the results of several well-known comparable results in the literature. To illustrate our results, we conclude the paper with some examples.

In this paper we establish some new Tauberian theorems for the statistical weighted mean method of summability via the weighted general control modulo of the oscillatory behavior of nonnegative integer order of a real sequence. The main results improve the well-known classical Tauberian theorems which are given for weighted mean method of summability and statistical convergence.

In this paper, we characterize the compact, invertible, Fredholm and closed range multiplication operators on Ces?ro function spaces.

In this paper we study fuzzy hyperideals of a fuzzy hyperring, we define and analyze two particular kinds of fuzzy hyperideals, which extend similar notions of ring context, namely prime fuzzy hyperideals and maximal fuzzy hyperideals. Moreover, we study the hyperideal transfer through a fuzzy hyperring homomorphism, particularly for prime fuzzy hyperideals and for maximal fuzzy hyperideals.

In this paper, we prove existence and uniqueness results for common fixed points of two or three relatively asymptotically regular mappings satisfying the orbital continuity of one of the involved maps on ordered orbitally complete metric spaces under generalized ?-contractive condition. Also, we introduce and use orbitally dominating maps and orbitally weakly increasing maps. We furnish suitable examples to demonstrate the usability of the hypotheses of our results. As an application, we prove the existence of solutions for certain system of integral equations.

Let K : [0,T0)? F be a locally integrable function, and C : X ? X a bounded linear operator on a Banach space X over the field F(=R or C). In this paper, we will deduce some basic properties of a nondegenerate local K-convoluted C-cosine function on X and some generation theorems of local Kconvoluted C-cosine functions on X with or without the nondegeneracy, which can be applied to obtain some equivalence relations between the generation of a nondegenerate local K-convoluted C-cosine function on X with subgenerator A and the unique existence of solutions of the abstract Cauchy problem: U''(t)=Au(t)+f(t) for a.e. t ? (0, T0), u(0) = x, u'(0) = y when K is a kernel on [0, T0), C : X ? X an injection, and A : D(A) ? X ? X a closed linear operator in X such that CA ? AC. Here 0 < T0 ? ?, x,y ? X, and f ? L1,loc([0,T0),X).

Let $\mathcal H$ be a complex Hilbert space and let $A$ be a bounded linear transformation on $\mathcal H$ . For a complex-valued function $f$ , which is analytic in a domain $\mathbb{D}$ of the complex plane containing the spectrum of $A$ , let $f(A)$ denote the operator on $\mathcal H$ defined by means of the \textit { Riesz - Dunford integral.} In the present paper, several (presumably new) versions of Pick's theorems are proved for $f(A),$ where $A$ is a dissipative operator (or a proper contraction) and $f$ is a suitable analytic function in the domain $\mathbb{D}$ .

In this paper we consider the notion of AI2-summability for real double sequences which is an extension of the notion of AI-summability for real single sequences introduced by Savas, Das and Dutta. We primarily apply this new notion to prove a Korovkin type approximation theorem. In the last section, we study the rate of AI2-summability.

In this paper, we discuss the following elliptic equation \begin{equation*} -\text{div}(\varphi(x,\nabla u))=\lambda f(x,u) \quad \textmd{in} \quad \Bbb R^{N}, \end{equation*} where the function $\varphi: \Bbb R^{N} \times \Bbb R^{N} \to \Bbb R^{N}$ is of type $|v|^{p-2}v$ with a real constant $p>1$ and $f:\Bbb R^{N}\times\Bbb R \to \Bbb R$ satisfies a Carath\'eodory condition. We show the existence of at least one nontrivial weak solution, and under suitable assumptions, infinitely many solutions for the problem above by using Mountain pass theorem and Fountain theorem. Also, we prove that the existence of at least two distinct nontrivial critical points under the appreciate assumptions.

Graded ditopological texture spaces have been presented and discussed in categorical aspects by Alexander Sostak and Lawrence M. Brown in [18]. In this paper, the authors study the generalization of two sorts of neighborhood structure defined in [10] to the graded ditopological texture spaces.

In this paper, we discuss the existence of fixed points for integral type contractions in uniform spaces endowed with both a graph and an E-distance. We also give two sufficient conditions under which the fixed point is unique. Our main results generalize some recent metric fixed point theorems.

In this paper we investigate the connection between the class SVs of slowly varying sequences (in the sense of Karamata) and the slow equivalence, strong asymptotic equivalence, selection principles and game theory.

In this paper we introduce and study of new types of connectedness in an ideal topological space. We also interrelate these connectedness with connectedness which are already in literature.

In this paper, first we prove the equivalence of the Frechet and the Jordan-Neumann relations in normed spaces. Next, we will present some characterizations of the inner product spaces and we will show their equivalence. Finally, we will prove some consequences of our main results.

In the present paper the authors introduce two new subclasses of multivalent analytic functions. Some properties such as distortion inequalities, inclusion relation, partial sums and convolution of functions belonging to these classes are given.

This paper is concerned with asymptotic analysis of positive decreasing solutions of the second-order quasilinear ordinary differential equation $$ \left(p(t)\f(|x'(t)|)\right)^\prime=q(t)\psi(x(t)),\leqno{\rm(E)} $$ with the regularly varying coefficients $p,\;q,\;\f,\;\psi$. An application of the theory of regularly variation gives the possibility of determining the precise information about asymptotic behavior at infinity of solutions of equation (E) such that $\dlim_{\tti} x(t)=0,\; \dlim_{\tti} p(t)\f(-x'(t))=\infty$.

In this paper, we investigate weighted asymptotic behavior of solutions to the Sobolev-type differential equation \begin{equation*} \frac{d}{dt}[u(t)+f(t,u(t))]=A(t)u(t)+g(t,u(t)), \ \ t\in \mathbb{R}, \end{equation*}% where $A(t) : D \subset \mathbb{X} \rightarrow \mathbb{X}$ for $t \in \mathbb{R}$ is a family of densely defined closed linear operator on a domain $D$, independent of $t$, and $f\ : \mathbb{R} \times \mathbb{X} \rightarrow \mathbb{X}$ is a weighted pseudo almost automorphic function and $g\ : \mathbb{R} \times \mathbb{X} \rightarrow \mathbb{X}$ is an $S^{p}$-weighted pseudo almost automorphic function and satisfying suitable conditions. Some sufficient conditions are established by properties of $S^{p}$-weighted pseudo almost automorphic functions combined with theories of asymptotically stable of operators.

WOS: 000355844100004, In this paper, we introduce and study new kinds of continuities. It turns out that a function f defined on an interval is uniformly continuous if and only if there exists a positive integer p such that f preserves p-quasi-Cauchy sequences where a sequence (x(n)) is called p-quasi-Cauchy if the sequence of differences between p-successive terms tends to 0.

The main result of this paper is a fixed point theorem for Matkowski type mapping with contractive iterate at a point in a class of G-metric spaces. Our result unifies, generalizes and complements some well known results in metric and G-metric spaces.

A categorical group is a kind of categorization of group and similarly a categorical ring is a categorization of ring. For a topological group X, the fundamental groupoid ?X is a group object in the category of groupoids, which is also called in literature group-groupoid or 2-group. If X is a path connected topological group which has a simply connected cover, then the category of covering groups of X and the category of covering groupoids of ?X are equivalent. Recently it was proved that if (X, x0) is an H-group, then the fundamental groupoid ?X is a categorical group and the category of the covering spaces of (X, x0) is equivalent to the category of covering groupoids of the categorical group ?X. The purpose of this paper is to present similar results for rings and categorical rings.

An ideal $I$ is a family of subsets of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. In this paper, we introduce the concepts of ideal $\tau$-convergence, ideal $\tau$-Cauchy and ideal $\tau$-bounded sequence in locally solid Riesz space endowed with the topology $\tau.$ Some basic properties of these concepts has been investigated. We also examine the ideal $\tau$-continuity of a mapping defined on locally solid Riesz space.

In this paper, a coincidence theorem is obtained which is generalization of Ky Fan?s fixed point theorem in modular function spaces. A modular version of Fan?s minimax inequality is proved. Moreover, some best approximation theorems are presented for multi-valued mappings.

In this paper, we prove some fixed point theorems for 1-monotone maps on partially ordered S-metric spaces. Our results generalize fixed point theorems in [1] and [7] for maps on metric spaces to the structure of S-metric spaces. Also, we give examples to demonstrate the validity of the results.

In the present paper the authors introduce two new subclasses of multivalent analytic functions. Distortion inequalities and partial sums of functions in these classes are given.

In the present paper, we derive several inclusion relationships and argument properties for certain classes of multivalent analytic functions associated with a family of linear operators involving the Srivastava-Khairnar-More operator. Furthermore, some invariant properties under convolution with convex functions for these classes are investigated. Relevant connections of the results presented here with those obtained in earlier works are also pointed out.

In this paper, we state a new form of fixed point theorems on metric spaces and 2-metric spaces which unifies and generalizes many results in the literature. Examples are given to illustrate the results.

In this paper, a generalized class of ??*called weakly Ir?-open sets in ideal topological spaces is introduced and the notion of weakly Ir?-closed sets in ideal topological spaces is studied. The relationships of weakly Ir?-closed sets and various properties of weakly Ir?-closed sets are investigated.