Fixed Point Theorems for Generalized R-Contraction in b-Metric Spaces

Atit Wiriyapongsanon, Narawadee Phudolsitthiphat

Abstract

In 2015, Roldan Lopez de Hierro and Shahzad introduced the family of R-functions which cover simulation function and manageable function. Following this line of research, we introduce a generalization of R-contraction in b-metric spaces and prove some fixed point theorems for such mappings in $b$-metric spaces. Our results extend and improve several well-known comparable results. Finally, we give examples to support our results.