Some Fixed Point Theorems in b-Metric Spaces with b-Simulation Functions

Benjawan Rodjanadid, Phuridet Cherachapridi, Jessada Tanthanuch

Abstract

The more generalized idea of the triangle inequality was introduced so that the concept of metric spacewas extended to b-metric space" in 1989 by Bakhtin. Many definitions and theories based on a metric space, e.g.convergent and cauchy sequences, a complete space, a simulation function, the contraction principle, the fixed point theorem,were considered in the $b$-metric space mentioned. In this article the notion of b-simulation function and generalized Z_b-contraction mapping were proposed.Also the proof the existence of a fixed point for such mapping in a complete b-metric space was presented.