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

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 εvariational-type principle, which generalizes the latter. As application, we study the existence of solution for a system of equilibrium problem.

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