• Communications of the Korean Mathematical Society
• /
• v.24 no.1
• /
• pp.17-27
• /
• 2009

In the present work, we introduce two types of compatible maps and prove a common fixed point theorem for such maps in Menger probabilistic metric spaces. Our result generalizes and extends many known results in metric spaces and fuzzy metric spaces.

• Communications of the Korean Mathematical Society
• /
• v.22 no.4
• /
• pp.513-526
• /
• 2007

In this paper, we give some new definitions of M-fuzzy metric spaces and we prove a common fixed point theorem for six mappings under the condition of compatible mappings of first or second type in two complete M-fuzzy metric spaces.

• Kyungpook Mathematical Journal
• /
• v.55 no.1
• /
• pp.205-218
• /
• 2015

In this paper, we introduce the concept of generalized c-distance on a cone metric space and prove some common fixed point and coincidence point results by using this notion. Our results generalize and extend several well known comparable results in the literature.

• Journal of applied mathematics & informatics
• /
• v.28 no.5_6
• /
• pp.1263-1275
• /
• 2010

In this paper, we introduce a new iterative scheme for finding a common element of the set of common fixed points of infinite family of nonexpansive mappings and the set of solutions to a generalized equilibrium problem and the set of solutions to a variational inequality problem in a real Hilbert space. Then strong convergence of the scheme to a common element of the three sets is proved. As applications, three new strong convergence theorems are obtained. Our theorems extend important recent results.

• East Asian mathematical journal
• /
• v.29 no.1
• /
• pp.23-37
• /
• 2013

The purpose of this paper is to study an implicit iteration process with errors and establish weak and strong convergence theorems to converge to common fixed points for a finite family of generalized asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. Our results extend, improve and generalize some known results from the existing literature.

• The Pure and Applied Mathematics
• /
• v.15 no.2
• /
• pp.135-151
• /
• 2008

The purpose of this paper is to prove some common fixed point theorems for finite number of discontinuous, noncompatible mappings on non complete Menger spaces. Our results extend, improve and generalize several known results in Menger spaces. We give formulas for total number of commutativity conditions for finite number of mappings.

• Communications of the Korean Mathematical Society
• /
• v.11 no.1
• /
• pp.89-108
• /
• 1996

In this paper we obtain common fixed point theorems for sequences of fuzzy mappings on Menger probabilistic metric spaces, including common fixed point theorems for sequences of multi-valued mappings, which generalize and improve some results of Lee et al. [8] and Chang [2].

• Korean Journal of Mathematics
• /
• v.26 no.4
• /
• pp.777-798
• /
• 2018

In this paper, we study a new iterative method for solving mixed equilibrium problem and a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the framework of reflexive real Banach spaces. Moreover, we prove a strong convergence theorem for finding common fixed points which also are solutions of a mixed equilibrium problem.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.4
• /
• pp.685-700
• /
• 2021

In this paper, we discuss the existence and uniqueness of fixed point and common fixed point theorems in complex valued extended b-metric spaces for a pair of mappings satisfying some rational contraction conditions which generalized and unify some well-known results in the literature.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.3
• /
• pp.603-620
• /
• 2022

Several common fixed point theorems for a pair of weakly compatible mappings satisfying contractive inequalities of integral type in a metric space are proved. The results obtained in this paper improve or differ from a few results existing in the literature.