In this paper, we introduce several types of correspondences: weakly naturally quasiconvex, *-weakly naturally quasiconvex, weakly biconvex and correspondences with *–weakly convex graph and we prove some fixed point theorems for these kinds of correspondences. As a consequence, using a version of W.K. Kim’s quasi-point theorem, we obtain the existence of equilibria for a quasi-game.

We show that quasi-metric or quasi-uniform spaces provide, inter alia, a common generalization of cpo's and metric spaces as used in denotational semantics. To accommodate the examples suggested by computer science, a reworking of basic notions involving limits and completeness is found to be necessary. Specific results include general fixed point theorem and a sequential completion construction.

The aim of this paper is to prove strong and △-convergence theorems of modified S-iterative scheme for asymptotically quasi-nonexpansive mapping in hyperbolic spaces. The results obtained generalize several results of uniformly convex Banach spaces and CAT(0) spaces. KeywordsHyperbolic space, fixed point, asymptotically quasi nonexpansive mapping, strong convergence, △-convergence.

We prove the weak and strong convergence of the implicit iterative process to a common fixed point of an asymptotically quasi-I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.

In this paper, we introduce the concepts of qpb-cyclic-Banach contraction mapping, qpb-cyclic-Kannan mapping and qpb-cyclic β-quasi-contraction mapping and establish the existence and uniqueness of fixed point theorems for these mappings in quasi-partial b-metric spaces. Some examples are presented to validate our results. c ©2016 All rights reserved.

In this paper, we presented new and important existence theorems of solution for quasi-equilibrium problems, and we show the uniqueness of its solution which is also a fixed point of some mapping. We show that this unique solution can be obtained by Picard's iteration method. We also get new minimax theorem, and existence theorems for common solution of fixed point and optimization problem on c...

The numerically exact superposition T-matrix method is used to model far-field electromagnetic scattering by two types of particulate object. Object 1 is a fixed configuration that consists of N identical spherical particles (with N=200 or 400) quasi-randomly populating a spherical volume V having a median size parameter of 50. Object 2 is a true discrete random medium (DRM) comprising the same...

In this paper, we first show that the iteration {xn} defined by xn+1 = P ((1−αn)xn +αnTP [βnTxn + (1− βn)xn]) converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with err...

The main aim of this paper is to study and establish some new coincidence point and common fixed point theorems in the product spaces of complete quasi-ordered metric spaces. The fixed point theorems in the product spaces will be the special case of coincidence point theorems in the product spaces. We also show that the concept of fixed point theorems in the product spaces extends the concept o...

This paper deals with a system of quasi-variational inequalities with noncoercive operators. We prove the existence of a unique weak solution using a lower and upper solutions approach. Furthermore, by means of a Banach’s fixed point approach, we also prove that the standard finite element approximation applied to this system is quasi-optimally accurate in L∞.