A generalized variational principle in b-metric spaces

Abstract

In this paper we establish and prove a generalized variational principle for b-metric spaces. As a consequence, we obtain a weak Zhong-type variational principle in b-metric spaces. We show the applicability of the mentioned generalized variational principle by presenting a Caristi-type fixed point theorem and an extension of the main result for bifunctions - both of them stated in b-metric spaces.

Keywords

• b-metric
• Ekeland-type variational principles
• Zhong-type variational principles
• Caristi's fixed point theorem