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 nonexpansive 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 Carath?odory?s type is considered in the framework of modular metric spaces.

Meir-Keeler type contractions on modular metric spaces

“…Following this initial results, a number of authors have reported several fixed point results for certain mappings in modular metric spaces, see e.g. [1,7,10] and related references therein.…”

Solvability of Fractional Differential Inclusion with a Generalized Caputo Derivative

“…An important role is played by the fixed-point principle to obtain the solvability of various types of operator equations (see, for example, [25][26][27][28][29]). We will apply the following fixed-point theorem to obtain the main results.…”

Cyclic $(\alpha ,\beta )$-Admissible Mappings in Modular Spaces and Applications to Integral Equations

“…Firstly, Nakano initiated the concept of modulared spaces [25]. Later, some authors proved new fixed point theorems of Banach type in modular spaces [1,13,16,20,21,32,2,3,5,8,9,10,12,14,19,23,28,29,33]. In this work, we present some fixed point results as a generalization of Banach's fixed point theorem using some convenient constants in the contraction assumption in modular spaces.…”