Fixed Point Theorems in Complete Modular Metric Spaces and an Application to Anti-periodic Boundary Value Problems

Abstract

In this paper existence and uniqueness of fixed points for a general class of contractive and non-expansive mappings on modular metric spaces is discussed.
As an application of the theoretical results, the existence of a solution of anti-periodic boundary value problems for nonlinear first order differential equations of Caratheodory's type is considered in he framework of modular metric spaces.