Vectorial form of Ekeland-type variational principle with applications to vector equilibrium problems and fixed point theory

Critical Point Theorems and Ekeland Type Variational Principle with Applications

We introduce the notion of λ-spaces which is much weaker than cone metric spaces defined by Huang and X. Zhang 2007 . We establish some critical point theorems in the setting of λ-spaces and, in particular, in the setting of complete cone metric spaces. Our results generalize the critical point theorem proposed by Dancs et al. 1983 and the results given by Khanh and Quy 2010 to λ-spaces and con...

Vectorial Form of Ekeland-Type Variational Principle in Locally Convex Spaces and Its Applications

By using a Danes̆’ drop theorem in locally convex spaces we obtain a vectorial form of Ekelandtype variational principle in locally convex spaces. From this theorem, we derive some versions of vectorial Caristi-Kirk’s fixed-point theorem, Takahashi’s nonconvex minimization theorem, and Oettli-Théra’s theorem. Furthermore, we show that these results are equivalent to each other. Also, the existen...

On Fixed Point Results for Hemicontractive-type Multi-valued Mapping, Finite Families of Split Equilibrium and Variational Inequality Problems

In this article, we introduced an iterative scheme for finding a common element of the set of fixed points of a multi-valued hemicontractive-type mapping, the set of common solutions of a finite family of split equilibrium problems and the set of common solutions of a finite family of variational inequality problems in real Hilbert spaces. Moreover, the sequence generated by the proposed algori...

Equilibrium problems and fixed point problems for nonspreading-type mappings in hilbert space

In this paper by using the idea of mean convergence, weintroduce an iterative scheme for finding a common element of theset of solutions of an equilibrium problem and the fixed points setof a nonspreading-type mappings in Hilbert space. A strongconvergence theorem of the proposed iterative scheme is establishedunder some control conditions. The main result of this paper extendthe results obtain...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points