Abstract
In this paper, we present a Pata-type fixed point theorem in modular spaces which generalizes and improves some old results. As an application, we study the existence of solutions of integral equations in modular function spaces.
Highlights
Introduction and preliminaries InNakano [ ] introduced the theory of modular spaces in connection with the theory of ordered spaces
There exists an extensive literature on the topic of the fixed point theory in modular spaces and the papers referenced there
Using the idea of Pata, we prove a fixed point theorem in modular spaces
Summary
Introduction and preliminaries InNakano [ ] introduced the theory of modular spaces in connection with the theory of ordered spaces. Using the idea of Pata, we prove a fixed point theorem in modular spaces. We prepare an application of our main results to the existence of solutions of integral equations in Musielak-Orlicz spaces.
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