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

The more generalized idea of the triangle inequality was introduced so that the concept of metric space was 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 spaces mentioned. In this article the notions of b-simulation functions and generalized Z(b)-contraction mappings were proposed. Also the existence of a fixed point for such a mapping in a complete b-metric space was presented.