In this note, we define Meir-Keeler contraction in S b -metric spaces. Further, by adding the concept of id="M4"> α -admissible mappings, generalized id="M5"> s -Meir-Keeler and used it for examining existence uniqueness fixed points. Various results are also given...

The theory of fixed point is a very extensive field, which has various applications. The present paper deals with some developments of Meir-Keeler type fixed point theorem as its remarkable generalizations under several contractive definitions in metric space.

We introduce a new iterative scheme with Meir-Keeler contractions for strict pseudocontractions in q-uniformly smooth Banach spaces. We also discuss the strong convergence theorems for the new iterative scheme in q-uniformly smooth Banach space. Our results improve and extend the corresponding results announced by many others.

In this paper we prove strong convergence theorems for approximating the fixed point of Lipschitzian semigroup and infinite family of nonexpansive mappings with respect to finite family of sequence {μi,n} ∞ i=1,n=1 of left strong regular invariant means and Meir-Keeler type contraction in uniformly convex and smooth Banach spaces. Our result extend and improve many recent results.

In this article, the notion of rational interpolative Meir-Keeler type contraction is discussed. The existence and uniqueness a fixed point for Das-Gupta are investigated. obtained results improve generalize existing on topic in recent literature.