A Common Fixed Point Theorem in Fuzzy Metric Spaces with Nonlinear Contractive Type Condition Defined Using Φ-Function

This paper is to present a common fixed point theorem for two R-weakly commuting self-mappings satisfying nonlinear contractive type condition defined using a Φ-function, defined on fuzzy metric spaces. Some comments on previously published results and some examples are given

A fixed point theorem in strictly convex b-fuzzy metric spaces

The main motivation for this paper is to investigate the fixed point property for non-expansive mappings defined on $b$-fuzzy metric spaces. First, following the idea of S. Ješić's result from 2009, we introduce convex, strictly convex and normal structures for sets in $b$-fuzzy metric spaces. By using topological methods and these notions, we prove the existence of fixed points for self-mappings defined on $b$-fuzzy metric spaces satisfying a nonlinear type condition. This result generalizes and improves many previously known results, such as W. Takahashi's result on metric spaces from 1970. A representative example illustrating the main result is provided

Common Fixed Points Theorems for Self-Mappings in Menger PM-Spaces

The purpose of this paper is to prove that orbital continuity for a pair of self-mappings is a necessary and sufficient condition for the existence and uniqueness of a common fixed point for these mappings defined on Menger PM-spaces with a nonlinear contractive condition. The main results are obtained using the notion of R-weakly commutativity of type Af (or type Ag). These results generalize some known results

Common Fixed Points Theorems for Self-Mappings in Menger PM-Spaces

The purpose of this paper is to prove that orbital continuity for a pair of self-mappings is a necessary and sufficient condition for the existence and uniqueness of a common fixed point for these mappings defined on Menger PM-spaces with a nonlinear contractive condition. The main results are obtained using the notion of R-weakly commutativity of type Af (or type Ag). These results generalize some known results