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In this paper, the complete moment convergence and the integrability of the supremum for weighted sums of negatively orthant dependent (NOD, in short) random variables are presented. As applications, the complete convergence and the Marcinkiewicz-Zygmund type strong law of large numbers for NODrandom variables are obtained. The results established in the paper generalize some corresponding ones for independent random variables and negatively associated random variables.

The aim of this paper is to understand how disruptions effect on closed-loop supply chain, and how to achieve the coordination of closed-loop supply chain under disruptions situation for the whole supply chain system. Design/methodology/approach- This paper analyzed the effect caused by the disruptions of the closed-loop supply chain from both supply and demand , and applied the established margin profits sharing contract to achieve coordination under the disruptions. Findings- From both supply side and demand side, it drew how the disruptions affect the closed-loop supply chain. When the disruptions have less effect on the forward and reverse cost of closed-loop supply chain, the impact of the closed-loop supply chain is controllable; when the disruptions have lager effect on the forward and reverse cost of closed-loop supply chain, the impact of the closed-loop supply chain is uncontrollable. Research limitations/implications- In this paper, the contract costs are ignored for zero. While in actual situation, to maintain the efficient implementation of this contract must spend considerable cost. Sometimes the cost may be too high to become hinder between manufacturers and retailers. This paper also does not make in-depth study on this issue, so it will be further study in the future. Originality/value- This paper also designed a set of differential profit sharing contract based on revenue sharing contract mechanism. The contract is easy to be managed, easy to be operated, making the closed-loop supply chain system can achieve coordination whether in steady state or under disruptions.

This paper which introduces the transaction concession strategy expands the artificial credit market model based on agent. First, through the investment and financing decision model, analysis the feasible set of the loan interest rate pricing in credit market. Second, proposed the bargaining decision mechanism of credit market based on concession strategy. Then we carried out simulation experiments on the artificial credit market based on concession strategy. The bilateral financial contract bargaining pricing mechanism under single issue frame in this paper provides fundamental ideas for optimizing the operation mechanism of credit market and improving credit market performance.

In this paper we study the geometry of relative superior Mandelbrot sets through S-iteration scheme. Our results are quit significant from other Mandelbrot sets existing in the literature. Besides this, we also observe that S-iteration scheme converges faster than Ishikawa iteration scheme. We believe that the results of this paper can be inspired thosewho are interested in creating automatically aesthetic patterns.

In this paper we survey the 3D reconstruction of an object from its 2D cross-sections has many applications in different fields of sciences such as medical physics and biomedical applications. The aim of this paper is to give not only the Bezier curves in medical applications, but also by using generating functions for the Bernstein basis functions and their identities, some combinatorial sums involving binomial coefficients are deriven. Finally, we give some comments related to the above areas.

The goal of the present paper is to study an extension problem of a connected preserving (for short, CP-) map between Khalimsky (K-for brevity, if there is no ambiguity) spaces. As a generalization of a K-continuous map, for K-topological spaces the recent paper [13] develops a function sending connected sets to connected ones (for brevity, an A-map: see Definition 3.1 in the present paper). Since this map plays an important role in applied topology including digital topology, digital geometry and mathematical morphology, the present paper studies an extension problem of a CP-map in terms of both an A-retract and an A-isomorphism (see Example 5.2). Since K-topological spaces have been often used for studying digital images, this extension problem can contribute to a certain areas of computer science and mathematical morphology.

The population of China has been aging quickly in recent years, which will profoundly affect the housing market. This paper aims to analyze the effect of aging on urban housing demand. First, a general equilibrium model with an overlapping generation structure is established to analyze theoretically the effect of aging. Then, this paper uses GAMS software to simulate and forecast the change trend in urban housing demand. Finally, based on the research sample of 287 large and medium-sized cities in China in 2010, this paper uses ArcGis9.3 software to study empirically the influence of aging on urban housing demand and concludes that aging can increase urban housing demand.

For analytic functions in the open unit disk $\mathbb U$ , we introduce a general family of integral operators. The main object of the this paper is to present a systematic study if this general family of integral operators and to determine the associated univalence conditions. Relevant connections of the results derived in this paper with those in several earlier works are also indicated.

This paper aims at studying the fundamental properties of fuzzy linear relations between vector spaces. The sum of two fuzzy relations and the scalar multiplication are defined, in a natural way, and some properties of this operations are established. Fuzzy linear relations are investigated and among the results obtained, there should be underlined a characterization of fuzzy linear relations and the fact that the inverse of a fuzzy linear relation is also a fuzzy linear relation. Moreover, the paper shows that the composition of two fuzzy linear relations is a fuzzy linear relation as well. Finally, the article highlights that the family of all fuzzy linear relations is closed under addition and it is closed under scalar multiplication.

Recently Srivastava et al. (26) introduced the incomplete Pochhammer symbols by means of the incomplete gamma functions (s; x) and (s; x), and defined incomplete hypergeometric functions whose a number of interesting and fundamental properties and characteristics have been investigated. Further, Cetinkaya (6) introduced the incomplete second Appell hypergeometric functions and studied many interesting and fundamental properties and characteristics. In this paper, motivated by the above- mentioned works, we introduce two incomplete Srivastava's triple hypergeometric functions H and H by using the incomplete Pochhammer symbols and investigate certain properties, for example, their various integral representations, derivative formula, reduction formula and recurrence relation. Various (known or new) special cases and consequences of the results presented here are also considered. 1. Introduction, Definitions and Preliminaries Throughout this paper, N, Z , and C denote the sets of positive integers, negative integers, complex numbers, respectively, and N0 := N(f0g and Z 0 := Z (f0g. The familiar incomplete Gamma functions (s; x) and (s; x) defined by

This paper is concerned with the existence and uniqueness of extremal solution for a nonlinear boundary value problems of fractional differential equation involving Riemann-Liouville derivative and p-Laplacian operator. By applying monotone iterative technique and lower and upper solutions method, we obtain sufficient conditions for the existence and uniqueness of extremal solution and construct the sequences of iteration to approximate it. The paper extends the applications of lower and upper solutions method and obtains some new results.

The aim of this paper is to continue our investigations in line of our recent paper, Savas [24] and [26]. We introduce the notion of AI-double statistical convergence which includes the new summabilitymethods studied in [24] and [23] as special cases and make certain observations on this new and moregeneral summability method. © 2016, University of Nis. All rights reserved.

Since a locally finite topological structure plays an important role in the fields of pure and applied topology, the paper studies a special kind of locally finite spaces, so called a space set topology (for brevity, SST) and further, proves that an SST is an Alexandroff space satisfying the separation axiom T0. Unlike a point set topology, since each element of an SST is a space, the present paper names the topology by the space set topology. Besides, for a connected topological space (X,T) with |X| = 2 the axioms T0, semi-T1/2 and T1/2 are proved to be equivalent to each other. Furthermore, the paper shows that an SST can be used for studying both continuous and digital spaces so that it plays a crucial role in both classical and digital topology, combinatorial, discrete and computational geometry. In addition, a connected SST can be a good example showing that the separation axiom semi-T1/2 does not imply T1/2.

Earned Value Method (EVM) is a project management technique for measuring both project progress and performance in project activities. Unfortunately, this method could not provide credible data in project progress measurement these days due to its deficiency. Thus, a new method called Earned Schedule (ES) is designed to cover EVMs limitation. Considering the fact that researches on ES are focus on simply project under certainty, this paper is to fill in the blank of uncertainty. In this paper, a new concept called interrupted Earned Schedule (iES) and its indicators are presented considering the situation of interrupted schedule when doing project progress measurement. This concept can offer accurate description about schedule interrupted project of its progress measurement. With the help of a model project, iES and its indicators are proven practicable. Moreover, a comparison between iES and ES of a schedule interrupted project shows priority of the former one.

With the deepening of new urbanization, local government debt risk in China is accumulating and amplifying. This paper first constructs local government debt risk index system and utilizes factor analysis to calculate the overall debt risk interval. Secondly, this paper builds a micro cash flow model based on genetic algorithm to estimate the reasonable scale of future borrowing under the cash flow constraint and risk index constraints. The objective is to achieve the optimal disposable revenue of local government. The model not only estimates the total borrowing scale, but also forms the different strategies of issuing bonds at different times and with different maturities. At the same time, we can change specific parameters (such as land transfer revenue) to analyse the variation of the future debt scale. Finally, this paper carries on an empirical study of city X to testify the methods and models, which provides scientific management of local government debt in the process of new urbanization.

In the wave of globalization, central parts of large cities are growing exponentially. As the phenomenon is expected to continue, the city and the state are expected to compete with each other in the future. However, the main factor that influences urban competitiveness, construction of infrastructure, continues to put decision-makers in cities in a dilemma. This paper uses data from the national bureau of economic analysis, the World Bank and the OECD to analyse the relationship between urban infrastructure investment and GDP, infrastructure investment as the proportion of real estate investment, the relationship between urban infrastructure construction investment and urbanization rate and per capita GDP. The above analysis leads to the finding that the channels match with all kinds of urban infrastructure investment and financing. Moreover, under perspective of cost management, the choice of investment and financing channels is analyzed. Simultaneously, the corresponding processes, principles and requirements in cost management are elaborated. This paper provides references for countries choosing different investment and financing channels.

In this paper, we consider the class of p-convex functions. We derive some new integral inequalities of Hermite-Hadamard and Simpson type for differentiable p-convex functions using two new integral identities. Some special cases are also discussed. Interested readers may find novel and innovative applications of p-convex functions in various branches of pure and applied sciences. The ideas and techniques of this paper may stimulate further research in this field.

In this paper, we show that the generalized Aluthge transformations of a large class of operators (weighted conditional type operators) are normal. As a consequence, the operatorMwEMu is p-hyponormal if and only if it is normal, and under a weak condition, if MwEMu is normal, then the Holder inequality turn into equality for w; u. Also, we give some applications of p-hyponormal weighted conditional type operators, for instance, point spectrum and joint point spectrum of p-hyponormal weighted conditional type operators are equal. In the end, some examples are provided to illustrate concrete application of the main results of the paper. This article has been retracted. Link to the retraction 10.2298/FIL1601253E

In this paper, two kinds of system of fuzzy differential inclusions are introduced and studied. An existence of the solutions for one system of fuzzy differential inclusions is proved by using continuous selection theorem. An existence of the solutions for another system of fuzzy differential inclusions is also proved by employing the fixed point theorem in the generalized metric space. The results presented in this paper improve and extend some known results concerned with the multivalued Cauchy problem and fuzzy differential inclusions.

In this paper, new Hermite-Hadamard type inequalities for n-times differentiable log-preinvex functions are established. The established results generalize some of those results proved in recent papers for differentiable log-preinvex functions and differentiable log-convex functions.

Vanishing of linearly independent curvature tensors of a non-symmetric affine connection space as functions of vanished curvature tensor of the associated space of this one are analyzed in the first part of this paper. Projective curvature tensors of a non-symmetric affine connection space are expressed as functions of the affine connection coefficients and Weyl projective tensor of the corresponding associated affine connection space in the second part of this paper.

In this paper we study the notion of a graded $\Omega$-group $(X,+,\Omega),$ but graded in the sense of M.~Krasner, i.e., we impose nothing on the grading set except that it is nonempty, since operations of $\Omega$ and the grading of $(X,+)$ induce operations (generally partial) on the grading set. We prove that graded $\Omega$-groups in Krasner's sense are determined up to isomorphism by their homogeneous parts, which, with respect to induced operations, represent partial structures called $\Omega$-\emph{homogroupoids}, thus narrowing down the theory of graded $\Omega$-groups to the theory of $\Omega$-homogroupoids. This approach already proved to be useful in questions regarding A. V. Kelarev's $S$-graded rings inducing $S,$ where $S$ is a partial cancellative groupoid. Particularly, in this paper we prove that the homogeneous subring of a Jacobson $S$-graded ring inducing $S$ is Jacobson under certain assumptions. We also discuss the theory of prime radicals for $\Omega$-homogroupoids thus extending results of A.~V.~Mikhalev, I.~N.~Balaba and S.~A.~Pikhtilkov in a natural way. We study some classes of $\Omega$-homogroupoids for which the lower and upper weakly solvable radicals coincide and also, study the question of the homogeneity of the prime radical of a graded ring.

Motivated by a recent paper, in which the authors studied Re-nnd {1,3}-inverse, {1,4}-inverse and {1,3,4}-inverse of a square matrix, in this paper, we establish some equivalent conditions for the existence of Re-nnd {1,2,3}-inverse, {1,2,4}-inverse and {1,3,4}-inverse. Furthermore, some expressions of these generalized inverses are presented.

In this paper, we mainly give much simple proof to Theorem 1.1 and (1.6) of Theorem 1.2 posed in the paper ?F. Qi, Limit formulas for ratios between derivatives of the gamma and digamma functions at their singularities, Filomat 27 (2013) 601-604.?

In this paper, we study the symmetric generalized quasi-variational inclusion problems. Then, we establish some existence theorems of solution sets for these problems. Moreover, the stability of solutions for these problems are also onbtained. Finally, we apply these results to symmetric vector quasi-equilibrium problems. The results presented in this paper improve and extend the main results in the literature. Some examples are given to illustrate our results.

In this paper we point out that a number of fixed point papers, involving several maps, are special cases of a general result proved several years ago by the author and G. F. Jungck, and one proved by Aliouche and Popa [1].

In this paper, we introduce and investigate three interesting subclass $\Sigma_\vartheta^*(\lambda,\alpha)$, $\Sigma_\vartheta^B(\beta,\alpha)$ and $\tilde{\Sigma}_\vartheta^*(\alpha,\beta)$ of meromorphic and bi-univalent functions on $\Delta=\{z\in\mathbb{C}: |z|>1\}$, obtain their coefficient estimates. The results presented in this paper generalize the recent work S.A.Halim et al.[1].

In this paper we study the existence and the uniqueness of isoperimetric extremals of rotation on two-dimensional (pseudo-) Riemannian manifolds and on surfaces on Euclidean space. We find the new form of their equations which is easier than results by S. G. Leiko. He introduced the notion of rotary diffeomorphisms. In this paper we propose a new proof of the fundamental equations of rotary mappings.

In this paper, we prove some Hermite-Hadamard inequalities for the class of relative semiconvex functions. Several special cases are also discussed. Thus it is worth mentioning that our results can be viewed as a generalization of previous results. Some applications to special means are also presented. Ideas and techniques of this paper may inspire further research in various branches of pure and applied sciences.

The objective of this paper is to obtain some Hermite-Hadamard type inequalities for h-preinvex functions. Firstly, a new kind of generalized h-convex functions, termed h-preinvex functions, is introduced through relaxing the concept of h-convexity introduced by Varosanec. Some Hermite-Hadamard type inequalities for h-preinvex functions are established under certain conditions. Our results can be viewed as generalization of several previously known results. Results proved in this paper may stimulate further research in different areas of pure and applied sciences.

In the paper [32], we have defined the concepts of lacunary statistical convergence of order ? and strong N?(p)-summability of order ? for sequences of complex (or real) numbers. In this paper we continue to examine others relations between lacunary statistical convergence of order ? and strong N?(p)-summability of order ?.

In this paper we discuss the subadditivity property of some auxiliary functions which have been used to generalize the contractive conditions on maps. Our results show that this property is not required in many cases and therefore, can be removed. We emphasize that in several papers (see e.g.[1]-[11]) dealing with such contraction mappings, the hypotheses of the main theorems can be restated in the light of our results.

In this paper some important variations and generalizations of the well-known Karamata?s integral theorem are proved. The property of rapid variability is the central argument for the results presented in this paper.

In this paper, we introduce a new iterative method for finding a common element of the set of solution of a general equilibrium problem system (GEPS) and the set of fixed points of a nonexpansive semigroup. Furthermore, we present some numerical examples (by using MATLsoftware) to guarantee the main result of this paper.

In this paper we consider concircular vector fields of manifolds with non-symmetric metric tensor. The subject of our paper is an equitorsion concircular mapping. A mapping f : GRN?GRN? is an equitorsion if the torsion tensors of the spaces GRN and GRN? are equal. For an equitorsion concircular mapping of two generalized Riemannian spaces GRN and GRN, we obtain some invariant curvature tensors of this mapping Z?,? = 1,2,... 5, given by equations (3.14, 3.21, 3.28, 3.31, 3.38). These quantities are generalizations of the concircular tensor Z given by equation (2.5).

In this paper, wefind necessary and sufficient conditions for Banach Space operator to satisfy the property(Bb). Thenweobtain,ifBanachSpaceoperatorsA ∈ B(X)andB ∈ B(Y)satisfyproperty(Bb)implies A⊗Bsatisfiesproperty(Bb)ifandonlyiftheB-Weylspectrumidentity σBW(A⊗B) = σBW(A)σ(B)∪σBW(B)σ(A) holds. Perturbations by Riesz operators are considered. Throughout this paper we denote by B(X) the algebra of all bounded linear operators acting on a Banach space X. For T ∈ B(X), let T ∗ ,ker(T) = T −1 (0), ℜ(T) = T(X), σ(T) and σa(T) denote respectively the adjoint, the null space, the range, the spectrum and the approximate point spectrum of T. Let α(T) and β(T) be the nullity and the deficiency of T defined by α(T) = dimker(T) and β(T) = codimℜ(T). If the range ℜ(T) of T ∈ B(X) is closed and α(T) < ∞ (resp., β(T) < ∞) then T is upper semi-Fredholm (resp., lower semi-Fredholm) operator. Let SF+(X) (resp.,SF−(X)) denote the semigroup of upper semi- Fredholm (resp., lower semi-Fredholm) operator on X. An operator T ∈ B(X) is said to be semi-Fredholm if T ∈ SF+(X) ∪ SF−(X) and Fredholm if T ∈ SF+(X) ∩ SF−(X). If T is semi-Fredholm then the index of T is defined by ind(T) = α(T) − β(T). Recall that the ascent of an operator T ∈ B(X) is the smallest non negative integer p:=p(T) such that T −p (0) = T −(p+1) (0). If there is no such integer, ie., T −p (0) , T −(p+1) (0) for all p, then set p(T) = ∞ . The descent of T is defined as the smallest non negative integer q:=q(T) such that T q (X) = T (q+1) (X). If there is no such integer, ie., T q (X) , T (q+1) (X) for all q, then set q(T) = ∞. It is well known that if p(T) and q(T) are both finite then they are equal (13, Proposition 38.6). A bounded linear operator T acting on a Banach space X is Weyl if it is Fredholm of index zero and Browder if T is Fredholm of finite ascent and descent. For T ∈ B(X), let , E 0 (T), and π 0 (T) denote, the eigenvalues of finite multiplicity and poles of T respectively . The Weyl spectrum σw(T) and Browder spectrum σb(T) of T are defined by σw(T) = { λ ∈ C : T − λ is not Weyl } , σb(T) = {λ ∈ C : T − λ is not Browder } . We have π 0 (T) := σ(T) \ σb(T). Set ∆(T) = σ(T) \ σw(T). According to Coburn (7), Weyl's theorem holds for T (abbreviation, T ∈ Wt) if ∆(T) = E 0 (T) and that Browder's theorem holds for T (in symbol, T ∈ Bt) if σ(T) \ σw(T) = π 0 (T).

In this paper we consider a problem that follows directly from realization problem: how to find Markovian representations , even minimall, for a given family of Hilbert spaces, understood as outputs of a stochastic dynamic system S1, provided it is in a certain causality relationship with another family of Hilbert spaces , i. e. with some informations about states of a stochastic dynamic system S2. This paper is continuation of the papers Gill and Petrovic [7] and Petrovic [16,17].

The research in this paper is a continuation of the investigation of the cardinality of the $��$-closed hull of subsets of spaces. This research obtains new upper bounds of the cardinality of the $��$-closed hull of subsets using cardinal functions of $��$-bitightness (\cite{Ca-Ko}), finite $��$-bitightness (\cite{Ca-Ca-Pa-Ts}) and $��$-bitightness small number (\cite{Ca-Ca-Pa-Ts}) of spaces. In the final section, examples of spaces are presented including one that answers a question posed in \cite{Bo-Ca-Ma} and \cite{Bo-Pa}., This paper has been withdrawn by the author due to an error in chapter 2

Let G be an (n,m)-graph (n vertices and m-regular) and H be an (m,d)-graph. Randomly number the edges around each vertex of G by {1, . . . ,m} and fix it. Then the replacement product GrH of graphs G and H (with respect to the numbering) has vertex set V(GrH) = V(G) ×V(H) and there is an edge between (v,k) and (w,l) if v = w and kl ∈ E(H) or vw ∈ E(G) and kth edge incident on vertex v in G is connected to the vertex w and this edge is the lth edge incident on w in G, where the numberings k and l refers to the random numberings of edges adjacent to any vertex of G. If the set of edges of a graph can be partitioned to a set of complete matchings, then the graph is called 1-factorizable and any such partition is called a 1-factorization. In this paper, 1-factorizability of the replacement product GrH of graphs G and H is studied. As an application we show that fullerene C60 and C4C8 nanotorus are 1-factorizable. Graphs considered in this paper are finite, simple and undirected. Let G be a simple graph. The vertex set, edge set, maximum degree and minimum degree of G will be denoted by V(G), E(G), ∆(G), δ(G) respectively. The order of G is |V(G)|, i.e. the number of vertices of G. A graph G is called regular if δ(G) = ∆(G) and the latter integer is called the degree of G and denoted by d(G). A d-regular graph G on n vertices is called an (n,d)-graph. A graph is called cubic if it is 3-regular. We denote by Kn and Cn the complete graph of order n and the cycle of order n, respectively. We denote by NG(x) the neighborhoods of x ∈ V(G), that is, the set of vertices adjacent to x.

In this paper, we introduce and investigate an interesting subclass N?h,p (?, ?) of analytic and bi-univalent functions in the open unit disk U. For functions belonging to the class N?h,p (?, ?), we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|. The results presented in this paper would generalize and improve some recent works of ?a?lar et al. [3], Xu et al. [10], and other authors.

The study of digital covering transformation groups (or automorphism groups, discrete deck transformation groups) plays an important role in the classification of digital spaces (or digital images). In particular, the research into transitive or nontransitive actions of automorphism groups of digital covering spaces is one of the most important issues in digital covering and digital homotopy theory. The paper deals with the problem: Is there a digital covering space which is not ultra regular and has an automorphism group which is not trivial? To solve the problem, let us consider a digital wedge of two simple closed ki-curves with a compatible adjacency, i ?{1,2}, denoted by (X, k). Since the digital wedge (X, k) has both infinite or finite fold digital covering spaces, in the present paper some of these infinite fold digital covering spaces were found not to be ultra regular and further, their automorphism groups are not trivial, which answers the problem posed above. These findings can be substantially used in classifying digital covering spaces and digital images so that the paper improves on the research in Section 4 of [3] (compare Figure 2 of the present paper with Figure 2 of [3]), which corrects an error that appears in the Boxer and Karaca's paper [3] (see the points (0,0), (0,8), (6, -1) and (6,7) in Figure 2 of [3]).

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

Recently, Filipovic et al. [M. Filipovic, L. Paunovic, S. Radenovic, M. Rajovic, Remarks on 'Cone metric spaces and fixed point theorems of T-Kannan and T-Chatterjea contractive mappings', Math. Comput. Modelling. 54 (2011) 1467-1472] proved several fixed and periodic point theorems for solid cones on cone metric spaces. In this paper several fixed and periodic point theorems for T-contraction of two maps on cone metric spaces with solid cone are proved. The results of this paper extend and generalize well-known comparable results in the literature.

Although Sumudu transform is the theoritical dual of the Laplace transform, it has many applications in sciences and engineering for its special fundamental properties. In a previous paper (3), we studied q-analogues of the Sumudu transform and derived some fundamental properties. This paper follows the previous paper and aims to provide some applications of the q-Sumudu transform. The authors give q-Sumudu transforms of some q-polynomials and q-functions. Also, we evaluated the q-Sumudu transform of basic analogue of Fox's H-function.

The aim of this paper is to study certain closure-type properties of function spaces over metric spaces endowed with two topologies: the topology of uniform convergence on a bornology and the topology of strong uniform convergence on a bornology. The study of function spaces with the strong uniform topology on a bornology was initiated by G. Beer and S. Levi in 2009, and then continued by several authors: A. Caserta, G. Di Maio and L'. Hol? in 2010, A. Caserta, G. Di Maio, Lj.D.R. Kocinac in 2012. Properties that we consider in this paper are defined in terms of selection principles.

In two BIT papers error expansions in the Gauss and Gauss-Tur´ an quadrature formulas with the Chebyshev weight function of the first kind, in the case when integrand is an analytic function in some region of the complex plane containing the interval of integration in its interior, have been obtained. On the basis of that, using a representation of the remainder term in the form of contour integral over confocal ellipses, the upper bound of the modulus of the remainder term, in the cases when certain parameter s (s ∈ N0) takes the specific values s = 0,1,2, has been obtained. Its form for a general s (s ∈ N0) has been supposed in one of the mentioned papers. Here, we prove that formula.

The problem of mean square bounded-input bounded-output(BIBO) stability is investigated for a class of discrete-time stochastic control systems with time delays and non-linear perturbations. In this paper, a special point δ in the time delay's variation interval is introduced, and the variation interval is dividedintotwosubintervals. Then,bydefiningaspecialLyapunov−Krasovskiifunctionalandcheckingits variationinthetwosubintervals,respectively,somenoveldelay-dependentstabilitycriteriaforthediscrete- time stochastic control systems are derived. These conditions are expressed in the forms of linear matrix inequalities(LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Meanwhile, this paper provides a new method for studying discrete-time stochastic mean square BIBO stability. Finally, a numerical example is given to illustrate the validity of the main results.

In this paper, parametric quintic spline method is presented to solve a linear special case sixth order two point boundary value problems with two different cases of boundary conditions. The method presented in this paper has been shown to be second and fourth order accurate. Boundary equations are derived for both the cases of boundary conditions. Convergence analysis of these methods are discussed. The presented method is tested on four numerical examples of linear sixth order boundary value problems. Comparison is made to show the practical usefulness of the presented method.

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.

The main object of this paper is to prove two general theorems by using a two-parameter quasi- f (?,?) -power increasing sequence instead of a quasi-?-power increasing sequence. The first result (Theorem 2.1) in this paper covers the case when 0 < ? < 1 and ? = 0. The second main result (Theorem 2.3) in this paper covers the exceptional case when ? = 1 and ? 5 0. Each of these theorems also includes several new or known results as their special cases and consequences.