Banach Contraction Principle-Type Results for Some Enriched Mappings in Modular Function Spaces

The idea of enriched mappings in normed spaces is relatively a newer idea. In this paper, we initiate the study of enriched mappings in modular function spaces. We first introduce the concepts of enriched (Formula presented.) -contractions and enriched (Formula presented.) -Kannan mappings in modular function spaces. We then establish some Banach Contraction Principle type theorems for the existence of fixed points of such mappings in this setting. Our results for enriched (Formula presented.) -contractions are generalizations of the corresponding results from Banach spaces to modular function spaces and those from contractions to enriched (Formula presented.) -contractions. We make a first ever attempt to prove existence results for enriched (Formula presented.) -Kannan mappings and deduce the result for (Formula presented.) -Kannan mappings. Note that even (Formula presented.) -Kannan mappings in modular function spaces have not been considered yet. We validate our main results by examples.