The Borwein-Preiss variational principle for nonconvex countable systems of equilibrium problems

Abstract

The aim of the present paper, by using the Borwein-Preiss variational principle, we prove existence results for countable systems of equilibrium problems. We establish some sufficient conditions which can guarantee two existence theorems for countable systems of equilibrium problems on closed subsets of complete metric spaces and on weakly compact subsets of real Banach spaces, respectively.

Ekeland’s Variational Principle and Minimization Takahashi’s Theorem in Generalized Metric Spaces

“…After presentation of Ekeland Variational Principle (EVP) in 1972, it becomes clear that this principle is equivalent to Caristi fixed point theorem [1][2][3][4][5][6][7][8][9], Drop theorem [10,11], Flower Petal theorem [10,11] and Takahashi's nonconvex minimization theorem. Many scholars have studied EVP on complete convex space and on locally convex space.…”