Yeol Je Cho

Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings

Abstract In the present paper, several weak and strong convergence theorems are established for the three-step iterative schemes with errors for asymptotically nonexpansive mappings. Our results extend and improve the recent ones announced by Tan and Xu, Xu and Noor, and many others.

Common fixed points of compatible maps of type (b) on fuzzy metric spaces

Abstract The purpose of this paper is to obtain some common fixed point theorems for compatible maps of type (β) on fuzzy metric spaces. Our results extend, generalize and fuzzify several fixed point theorems on metric spaces, Menger probabilistic metric spaces, uniform spaces and fuzzy metric spaces.

Nonlinear relaxed cocoercive variational inclusions involving (A, η )-accretive mappings in banach spaces

In this paper, we introduce a new concept of (A, @h)-accretive mappings, which generalizes the existing monotone or accretive operators. We study some properties of (A, @h)-accretive mappings and define resolvent operators associated with (A, @h)-accretive mappings. By using the new resolvent operator technique, we also construct a new perturbed iterative algorithm with mixed errors for a class of nonlinear relaxed Cocoercive variational inclusions involving (A, @h)-accretive mappings and study applications of (A, @h)-accretive mappings to the approximation-solvability of this class of nonlinear relaxed Cocoercive variational inclusions in q-uniformly smooth Banach spaces. Our results improve and generalize the corresponding results of recent works.

Sensitivity analysis for strongly nonlinear quasi-variational inclusions

Abstract In this paper, we use the implicit resolvent operator technique to study the sensitivity analysis for strongly nonlinear quasi-variational inclusions. Our results improve and generalize some of the recent ones.

Convergence of a modified Halpern-type iteration algorithm for quasi-ϕ-nonexpansive mappings

The purpose of this work is to modify the Halpern-type iteration algorithm to have strong convergence under a limit condition only in the framework of Banach spaces. The results presented in this work improve on the corresponding ones announced by many others.

Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems☆

In this paper, we present an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem and the set of fixed points of an infinite family of nonexpansive mappings and the set of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm has strong convergence under some mild conditions imposed on algorithm parameters.

Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type

In this article, we study coupled coincidence and coupled common fixed point theorems in ordered generalized metric spaces for nonlinear contraction condition related to a pair of altering distance functions. Our results generalize and modify several comparable results in the literature.2000 MSC: 54H25; 47H10; 54E50.

Common fixed point theorems in intuitionistic fuzzy metric spaces

The purpose of this paper, using the idea of intuitionistic fuzzy set due to Atanassov [2], we define the notion of intuitionistic fuzzy metric spaces (see, [1]) due to Kramosil and Michalek [17] and Jungck’s common fixed point theorem ([11]) is generalized to intuitionistic fuzzy metric spaces. Further, we first formulate the definition of weakly commuting and R-weakly commuting mappings in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant’s theorem ([21]).

Coincidence point theorems and minimization theorems in fuzzy metric spaces

Abstract In this paper, some new versions of coincidence point theorems and minimization theorems for single-valued and multi-valued mappings in generating spaces of the quasi-metric family are obtained. As applications, we utilize our main theorems to prove coincidence point theorems, fixed point theorems and minimization theorems for single-valued and multi-valued mappings in fuzzy metric spaces and probabilistic metric spaces.

Coupled coincidence point theorems for contractions without commutative condition in intuitionistic fuzzy normed spaces

Recently, Gordji et al. [Math. Comput. Model. 54, 1897-1906 (2011)] prove the coupled coincidence point theorems for nonlinear contraction mappings satisfying commutative condition in intuitionistic fuzzy normed spaces. The aim of this article is to extend and improve some coupled coincidence point theorems of Gordji et al. Also, we give an example of a nonlinear contraction mapping which is not applied by the results of Gordji et al., but can be applied to our results.2000 MSC: primary 47H10; secondary 54H25; 34B15.