New existence theorems of coincidence points approach to generalizations of Mizoguchi-Takahashi’s fixed point theorem

New existence theorems of coincidence points approach to generalizations of Mizoguchi-Takahashi’s fixed point theorem

*Correspondence: [email protected] Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, 824, Taiwan Abstract In this paper, we first establish some new existence theorems of coincidence points and common fixed points forMT -functions. By applying our results, we obtain some generalizations of Mizoguchi-Takahashi’s fixed point theorem, Nadler’s fixed point theorem a...

Some Generalizations of Mizoguchi-Takahashi’s Fixed Point Theorem

The main aim of this paper is to establish some generalizations of Mizoguchi-Takahashi’s fixed point theorem. Mathematics Subject Classification: 47H10, 54C10

New Existence Results and Generalizations for Coincidence Points and Fixed Points without Global Completeness

and Applied Analysis 3 (w3) for any ε > 0, there exists δ > 0 such that p(z, x) ≤ δ and p(z, y) ≤ δ imply d(x, y) ≤ ε. A function p : X×X → [0,∞) is said to be a τ-function [5, 10, 14, 15, 27–29], first introduced and studied by Lin and Du, if the following conditions hold: (τ1) p(x, z) ≤ p(x, y) + p(y, z) for all x, y, z ∈ X; (τ2) if x ∈ X and {yn} in X with limn→∞yn = y such that p(x, yn) ≤ M...

New Best Proximity Point Theorems with Applications to Simultaneous Generalizations of Common Fixed Point Theorems

In this work, we first introduce the concept of approximate sequence and establish some new convergence theorems for approximate sequences. By applying our new convergence theorems, we obtain new best proximity point theorems which improve and generalize some known results in the literature. As applications, some simultaneous generalizations of common fixed point theorems of Banach type, Kannan...

Some Generalizations of Jungck's Fixed Point Theorem