Abstract: We have established, in the context of metric spaces, that an F-contraction restricted to appropriate neighborhood of its fixed point is an almost contraction and obtain definition of retractions on complete metric spaces. We have illustrated such an inclusion using an example studied in Wardowski (Fixed Point Theory Appl 94:1–6, 2012) and in Minak et al. (Bull Belg Math Soc Simon Stevin 22:411–422, 2015). PubDate: 2019-03-15

Abstract: We consider the degenerate nonlinear elliptic equation (E) : \({\mathcal {A}}(u)= g-{\text {div}}(f)\) , where \({\mathcal {A}}(u)=-{\text {div}}(a(x,u,\nabla u))\) is a Leray-Lions operator defined on \(W_0^{1,p(\cdot )}(\Omega )\) allowed to be non linear degenerated. The main gaol of this paper is to prove in first, an \(L^{\infty }(\Omega )\) estimate for the bounded solution of (E), and then the existence of a weak and a renormalized solution of (E), with \(f\in (L^{r(\cdot )}(\Omega ))^N, g\in L^{q(\cdot )}(\Omega )\) , where \(r(\cdot )\) and \(q(\cdot )\) satisfies the following conditions : $$\begin{aligned} {\left\{ \begin{array}{ll} r(x)>\frac{N}{p(x)-1}, r(x)\ge p'(x)&{}\quad \forall x \in \Omega ,\\ q(x)>\max \left( \frac{N}{p(x)},1\right) , q(x)\ge p'(x)&{}\quad \forall x \in \Omega . \end{array}\right. } \end{aligned}$$ PubDate: 2019-03-14

Abstract: In this paper, a two-phase quasi-Newton scheme is proposed for solving an unconstrained optimization problem. The global convergence property of the scheme is provided under mild assumptions. The superlinear convergence rate of the scheme is also proved in the vicinity of the solution. The advantages of the proposed scheme over the traditional schemes are justified with numerical table and graphical illustrations. PubDate: 2019-03-12

Abstract: In this paper, an iterative method for multiple roots of nonlinear equations is presented. Its convergence order is analyzed and proved. It is shown that the proposed method has third-order convergence. To assess the validity and performance of the proposed method, some nonlinear equations are solved and the results are compared with the results from six other methods. PubDate: 2019-03-11

Abstract: In this paper, we prove some fixed point theorems by introducing a new F-contraction namely \(S_F\) -contraction in fuzzy metric spaces by combining the idea of Wardowski’s (Fixed Point Theory Appl 2012, Article ID 94, 2012) and Secelean’s (Fixed Point Theory Appl 2013, Article ID 277, 2013) contractions in metric spaces and Grabiec’s (Fuzzy Sets Syst 125, 385–389, 1988) contraction in fuzzy metric spaces. An example is also given to support the results proved herein. PubDate: 2019-03-08

Abstract: In this paper, we introduce a combination of family of some conjugate gradient methods (CG) with the trust-region method. Whenever the trust-region algorithm is unsuccessful, a family of CG methods is used to prevent resolving the trust-region subproblem. The computational cost for such a family is trivial. The global theory of the new approach is proved and numerical experiments are reported. PubDate: 2019-03-08

Abstract: This paper studies a duopoly investment model with uncertainty. There are two alternative irreversible investments. The first firm to invest gets a monopoly benefit for a specified period of time. The second firm to invest gets information based on what happens with the first investor, as well as cost reduction benefits. We describe the payoff functions for both the leader and follower firm. Then, we present a stochastic control game where the firms can choose when to invest, and hence influence whether they become the leader or the follower. In order to solve this problem, we combine techniques from optimal stopping and game theory. For a specific choice of parametres, we show that no pure symmetric subgame perfect Nash equilibrium exists. However, an asymmetric equilibrium is characterized. In this equilibrium, two disjoint intervals of market demand level give rise to preemptive investment behavior of the firms, while the firms otherwise are more reluctant to be the first mover. PubDate: 2019-03-07

Abstract: In this paper geometrical aspects of perfect fluid spacetime with torse-forming vector field \(\xi \) are described and Ricci soliton in perfect fluid spacetime with torse-forming vector field \(\xi \) are determined. Conditions for the Ricci soliton to be expanding, steady or shrinking are also given. PubDate: 2019-03-07

Abstract: In this investigation, in the light of the q-derivative operator and the q-analog of the well-known generalized Bessel function, several inequalities relating to Fekete–Szegö problems specified by the Hadamard product of certain meromorphic functions analytic in the punctured unit disc are first achieved and some consequences of them are then pointed out. PubDate: 2019-03-07

Abstract: Recently, George Andrews gave a detailed study of partitions with even parts below odd parts in which only the largest even part appears an odd number of times. In this note, we provide a combinatorial proof of a generating function identity related to such partitions. This answers a problem of Andrews. PubDate: 2019-03-06

Abstract: The aim of this paper is to give the predictable representation property associated with Lévy process in the non-homogeneous case. In this latter, we establish the existence and uniqueness of solution for the Backward Stochastic Differential Equations and its relation with Partial integro-differential equations. PubDate: 2019-03-05

Abstract: The notions of a s- \(T_1\) space, an almost generalized Hausdorff space, and a \(\mu \) -locally compact space in the context of generalized topological spaces are introduced. Properties in relation to these spaces are established. Finally, a version of one point compactification of a s- \(T_1\) space is obtained. PubDate: 2019-03-01

Abstract: In the present paper, we determine necessary and sufficient conditions for zF(a, b; c; z) and \(z(2-F(a,b;c;z))\) where \(F(a,b;c;z)=\sum \nolimits _{n=0}^{\infty }[(a)_{n}(b)_{n}/(c)_{n}(1)_{n}]z^{n}\) to be in a certain class of analytic functions with negative coefficients. Furthermore, we consider an integral operator related to hypergeometric functions. PubDate: 2019-03-01

Abstract: We consider abstract quasilinear evolution equations of Sobolev type in a Hilbert setting. We propose two fully discrete schemes and prove some error estimates under minimal assumptions. Various examples that enter into our abstract framework are considered, for each of them our theoretical results are confirmed by several numerical experiments. PubDate: 2019-03-01

Abstract: In this paper, we are mainly interested to find the sufficient conditions on parameters A, B, b and c that will ensure the generalized Struve function \( u_{v,b,c}\) satisfies the subordination \(u_{v,b,c}\left( z\right) \prec \left( 1+Az\right) /\left( 1+Bz\right) \) . PubDate: 2019-03-01

Abstract: In 1992, Blasco considered a weighted Bergman space using Dini-weight function. He proved that a linear operator T on weighted Bergman space to any Banach space X is bounded if and only if certain one parameter fractional derivative of a single X-valued analytic function satisfy some growth condition. In this paper, we use a three parameters fractional derivative of a single X-valued analytic function and provide an equivalent condition. Our technique uses the Gaussian hypergeometric functions. Furthermore we supply some conditions on the parameters a, b and c under which the Gaussian hypergeometric functions F(a, b; c; z) are Dini-weight. PubDate: 2019-03-01

Abstract: In this paper, we define some new number sequences, which we represent as \( (B_{n}),(b_{n}),(y_{n})\) and present relations of these new sequences with each other. Then, we give all positive integer solutions of some Diophantine equations in terms of these new sequences. PubDate: 2019-03-01

Abstract: The aim of the present article is to introduce a kind of proximity structure, termed \(\mu \) -proximity, on a set X, which ultimately gives rise to a generalized topology on the ambient set X. An alternative description of \(\mu \) -proximity is given and it is shown that any generalized topology of a generalized topological space \((X, \mu )\) is always induced by a suitable \(\mu \) -proximity if and only if \((X, \mu )\) satisfies a type of complete regularity condition. The notion of quasi \(\mu \) -proximity is also introduced and the desired result that every generalized topology can be achieved from a quasi \(\mu \) -proximity, is proved. PubDate: 2019-03-01

Abstract: We introduce the notion of congruences in hyperlattices. We prove that a quotient of a hyperlattice by a congruence is a “weak-hyperlattice” and not a hyperlattice in general. We explore the connections between congruences, ideals and homomorphism of hyperlattices. In particular, we establish necessary and sufficient conditions for a zero-congruence class to be an ideal of a hyperlattice. PubDate: 2019-03-01