𝓗-SIMULATION FUNCTIONS AND Ωb-DISTANCE MAPPINGS IN THE SETTING OF Gb-METRIC SPACES AND APPLICATION

Abstract

The conceptions of generalized b-metric spaces or Gb-metric spaces and a gener- alized Ω-distance mappings play a key role in proving many important theorems in existence and uniqueness of fixed point theory. In this manuscript, we establish a new type of contraction namely, Ωb(𝓗,θ,s)-contraction, this contraction based on the concept of a generalized Ω-distance mappings which established by Abodayeh et.al. in 2017 together with the concept of 𝓗-simulation functions which established by Bataihah et.al [10] in 2020. By utilizing this new notion we prove new results in existence and uniqueness of fixed point. On the other hand, examples and application were established to show the importance of our results.