Mizoguchi-Takahashi's Fixed Point Theorem Research Articles

A generalization of Mizoguchi-Takahashi's fixed point theorem and its applications to fixed point theory

A generalization of Mizoguchi-Takahashi's fixed point theorem and its applications to fixed point theory

Overall approach to Mizoguchi--Takahashi type fixed point results

In this work, inspired by the recent technique of Jleli and Samet, we give a new generalization of the wellknown Mizoguchi–Takahashi fixed point theorem, which is the closest answer to Reich’s conjecture about the existence of fixed points of multivalued mappings on complete metric spaces. We also provide a nontrivial example showing that our result is a proper generalization of the Mizoguchi–Takahashi result.

Fixed points of Mizoguchi–Takahashi contraction on a metric space with a graph and applications

In this paper we extend Mizoguchi–Takahashi's fixed point theorem for multi-valued mappings on a metric space endowed with a graph. As an application, we establish a fixed point theorem on an ε-chainable metric space for mappings satisfying Mizoguchi–Takahashi contractive condition uniformly locally. Also, we establish a result on the convergence of successive approximations for certain operators (not necessarily linear) on a Banach space as another application. Consequently, this result yields the Kelisky–Rivlin theorem on iterates of the Bernstein operators on the space C[0,1] and also enables us study the asymptotic behaviour of iterates of some nonlinear Bernstein type operators on C[0,1].

New Results and Generalizations for Approximate Fixed Point Property and Their Applications

We first introduce the concept of manageable functions and then prove some new existence theorems related to approximate fixed point property for manageable functions andα-admissible multivalued maps. As applications of our results, some new fixed point theorems which generalize and improve Du's fixed point theorem, Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, and Nadler's fixed point theorem and some well-known results in the literature are given.

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

Some new existence theorems concerning approximate coincidence point property and approximate fixed point property for nonlinear maps in metric spaces without global completeness are established in this paper. By exploiting these results, we prove some new coincidence point and fixed point theorems which generalize and improve Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, Kikkawa-Suzuki's fixed point theorem, and some well known results in the literature. Moreover, some applications of our results to the existence of coupled coincidence point and coupled fixed point are also presented.

On generalized weakly directional contractions and approximate fixed point property with applications

In this article, we first introduce the concept of directional hidden contractions in metric spaces. The existences of generalized approximate fixed point property for various types of nonlinear contractive maps are also given. From these results, we present some new fixed point theorems for directional hidden contractions which generalize Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem and some well-known results in the literature.

NONLINEAR CONDITIONS FOR COINCIDENCE POINT AND FIXED POINT THEOREMS

In this paper, we first establish some new types of fixed point theorem which generalize and improve Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem and many results in [W.-S. Du, Some new results and generalizations in metric fixed point theory, Nonlinear Anal. 73 (2010), 1439-1446] and references therein. Applying those new results, we also present some existence theorems of coincidence point and others.

On Approximate Coincidence Point Properties and Their Applications to Fixed Point Theory

We first establish some existence results concerning approximate coincidence point properties and approximate fixed point properties for various types of nonlinear contractive maps in the setting of cone metric spaces and general metric spaces. From these results, we present some new coincidence point and fixed point theorems which generalize Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, and some well-known results in the literature.

An extension of the Mizoguchi-Takahashi fixed point theorem

An extension of the Mizoguchi-Takahashi fixed point theorem

Fixed point theorems for multi-valued mappings obtained by altering distances

Recently T. Suzuki showed that the Mizoguchi–Takahashi fixed point theorem is a real generalization of Nadler’s fixed point theorem. Taking inspiration from the result of Mizoguchi and Takahashi and using the ideas of Feng and Liu, Klim and Wardowski obtained some fixed point theorems and showed that their results are different from the Reich point theorem and the Mizoguchi–Takahashi fixed point theorem. Very recently, Pathak and Shahzad introduced a class of functions and generalized some fixed point theorems of Klim and Wardowski by altering distances, i.e., via the mapping T (from a complete metric space ( X , d ) to the class of nonempty closed subsets of X ). In this paper we introduce a new class of functions which is a subclass of the class introduced by Pathak and Shahzad and improve some results of Pathak and Shahzad by allowing T to have values in closed subsets of X .

Some new results and generalizations in metric fixed point theory

The main purpose of this paper is the study of the generalization of some results given in [M. Berinde, V. Berinde, On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl. 326 (2007) 772–782] and references therein. Some generalizations of the Mizoguchi–Takahashi fixed point theorem, Kannan’s fixed point theorems and Chatterjea’s fixed point theorems are established by using our new fixed point theorems.

On the equivalence of the Mizoguchi–Takahashi fixed point theorem to Nadler’s theorem

In this work, we prove that on a metrically convex complete metric space, the Mizoguchi–Takahashi theorem is equivalent to Nadler’s theorem. Also, we obtain its equivalence on a compact metric space.

Mizoguchi–Takahashi's fixed point theorem is a real generalization of Nadler's

We give an example which says that Mizoguchi–Takahashi's fixed point theorem for set-valued mappings is a real generalization of Nadler's. We also give a very simple proof of Mizoguchi–Takahashi's theorem.