COMMON FIXED POINT AND INVARIANT APPROXIMATION IN MENGER CONVEX METRIC SPACES

Fixed Points and Best Approximation in Menger Convex Metric Spaces

Nonexpansive mappings have been studied extensively in recent years by many authors.The first fixed point theorem of a general nature for nonlinear nonexpansive mappings in noncompact setting were proved independently by Browder [8] and Gohde [12]. Later on, Kirk [17] proved the same results under slightly weaker assumptions. A fundamental problem in fixed point theory of nonexpansive mappings ...

Generalized Distance and Common Fixed Point Theorems in Menger Probablistic Metric Spaces

Common Fixed Point Theorems in Menger Spaces

In this paper Theorem 3.1 of Kubiaczyk and Sushil Sharma [5] is shown to hold even under weaker hypothesis (Theorem 2.2) and we obtain a fixed point theorem (Theorem 2.3) involving occasionally weakly compatible maps and also prove a coincidence point theorem (Theorem 2.4) for a pair of self maps under certain conditions. Examples are provided to show that the hypothesis in Theorems 2.3 and 2.4...

Common fixed point theorems in Menger spaces

Probabilistic metric space was first introduced by Menger [6]. Later, there are many authors who have some detailed discussions and applications of a probabilistic metric space, for example, we may see Schweizer and Sklar [8]. Besides, there are many results about fixed point theorems in a probabilistic metric space with contractive types having appeared; we may see the papers [1–3, 9–12]. In t...

Common fixed point and invariant approximations for subcompatible mappings in convex metric spaces

A common fixed point theorem for subcompatible mappings satisfying a generalized contractive condition (in the framework of a convex metric space) is proved and also utilized to derive some invariant approximation results. AMS subject classifications: 41A50, 47H10