Caristi’s Fixed Point Theorem and Ekeland’s Variational Principle for Set Valued Mapping using the LZ-functions

Abstract

The aims of this paper is to give some new theorems in the field of fixed point theory. For that, we establish a generalized result of Caristi's fixed point theorem by introducing a new type of functions that will be called the LZ-functions. And since that theorem is equivalent to Ekeland's variational principle, we derive also an ε-variational-type principle, which generalizes the latter. As application, we study the existence of solution for a system of equilibrium problem. General TermsFixed point