Abdul Latif

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 ρ-contractions and enriched ρ-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 ρ-contractions are generalizations of the corresponding results from Banach spaces to modular function spaces and those from contractions to enriched ρ-contractions. We make a first ever attempt to prove existence results for enriched ρ-Kannan mappings and deduce the result for ρ-Kannan mappings. Note that even ρ-Kannan mappings in modular function spaces have not been considered yet. We validate our main results by examples.

In this study, we present some new results on the existence of fixed points for multivalued generalized w b -contractive mappings in the frame work of metric type spaces. Consequently, presented results unify and generalize several known metric fixed-point results. In support of our main results, examples are provided to show that the results are genuine generalization of the known corresponding results of metric fixed-point theory.