Convex contraction-type mappings in modular metric spaces with applications

Purpose In this article, new contraction mappings are introduced in the context of modular metric spaces. Conditions for such operators to have fixed points are explained. The validity of the obtained results and their connection with the existing literature are demonstrated via a nontrivial example. From application perspectives, it is demonstrated that the concepts proposed herein enable the development of novel criteria for solving a class of integral equations. Design/methodology/approach The research adopts the classical method of proving fixed-point results of Lipschitzian mappings, using the Picard iteration. Findings Fixed-point results of several kinds of modular contraction-type inequalities are established in this article. An example is provided to bolster the theories developed by the findings reported here. Examining an application to an integral equation expressed as an invariant point problem demonstrates the research’s wide utility. Originality/value Fixed-point findings of modular contraction types and related applications are not given enough attention in the literature. Therefore, this work focuses on studying fixed point results of several kinds of modular contraction-type inequalities.