Wei-Shih Du

Coupled Fixed Point Theorems for Nonlinear Contractions Satisfied Mizoguchi-Takahashi's Condition in Quasiordered Metric Spaces

The main aim of this paper is to study and establish some new coupled fixed point theorems for nonlinear contractive maps that satisfied Mizoguchi-Takahashis condition in the setting of quasiordered metric spaces or usual metric spaces.

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-Berindes fixed point theorem, Mizoguchi-Takahashis fixed point theorem and some well-known results in the literature.MSC: 47H10; 54H25.

The existence of fixed points for new nonlinear multivalued maps and their applications

AbstractIn this paper, we first establish some new fixed point theorems for MT-functions. By using these results, we can obtain some generalizations of Kannans fixed point theorem and Chatterjeas fixed point theorem for nonlinear multivalued contractive maps in complete metric spaces. Our results generalize and improve some main results in the literature and references therein. Mathematics Subject Classifications 47H10; 54H25

Nonlinear Contractive Conditions for Coupled Cone Fixed Point Theorems

We establish some new coupled fixed point theorems for various types of nonlinear contractive maps in the setting of quasiordered cone metric spaces which not only obtain several coupled fixed point theorems announced by many authors but also generalize them under weaker assumptions.

Nonlinear algorithms approach to split common solution problems

In this paper, we introduce some new iterative algorithms for the split common solution problems for equilibrium problems and fixed point problems of nonlinear mappings. Some examples illustrating our results are also given.MSC:47J25, 47H09, 65K10.

Critical Point Theorems for Nonlinear Dynamical Systems and Their Applications

We present some new critical point theorems for nonlinear dynamical systems which are generalizations of Dancš-Hegedüs-Medvegyevs principle in uniform spaces and metric spaces by applying an abstract maximal element principle established by Lin and Du. We establish some generalizations of Ekelands variational principle, Caristis common fixed point theorem for multivalued maps, Takahashis nonconvex minimization theorem, and common fuzzy fixed point theorem for -functions. Some applications to the existence theorems of nonconvex versions of variational inclusion and disclusion problems in metric spaces are also given.

A note on Caristi-type cyclic maps: related results and applications

In this note, we first introduce the concept of Caristi-type cyclic map and present a new convergence theorem and a best proximity point theorem for Caristi-type cyclic maps. It should be mentioned that in our results, the dominated functions need not possess the lower semicontinuity property. Some best proximity point results and convergence theorems in the literature have been derived from our main results. Consequently, the presented results improve, extend and generalize some of the existence results on the topic.MSC:37C25, 47H09, 45H10, 54H25.

A note on cone b-metric and its related results: generalizations or equivalence?

Very recently, a notion of cone b-metric was introduced as a generalization of b-metric, and some related fixed point results were obtained. In this paper, we investigate the answer to the question whether the given results generalize the existing ones or are equivalent to them.MSC:46N40, 47H10, 54H25, 46T99.

The Study of Fixed Point Theory for Various Multivalued Non-Self-Maps

The basic motivation of this paper is to extend, generalize, and improve several fundamental results on the existence (and uniqueness) of coincidence points and fixed points for well-known maps in the literature such as Kannan type, Chatterjea type, Mizoguchi-Takahashi type, Berinde-Berinde type, Du type, and other types from the class of self-maps to the class of non-self-maps in the framework of the metric fixed point theory. We establish some fixed/coincidence point theorems for multivalued non-self-maps in the context of complete metric spaces.

Some generalizations of Mizoguchi-Takahashi's fixed point theorem with new local constraints

AbstractIn this paper, motivated by Kikkawa-Suzuki’s fixed point theorem, we establish some new generalizations of Mizoguchi-Takahashi’s fixed point theorem with new local constraints on discussion maps. MSC:47H10, 54C60, 54H25, 55M20.