Fixed Circle and Fixed Disc Results for New Types of Θ_c-Contractive Mappings in Metric Spaces

Abstract

In this manuscript, we introduce the notions of various types of Θc-contractions for which we establish some fixed circle and fixed disc theorems in the setting of metric spaces. Some illustrative examples are also provided to support our results. Moreover, we present some fixed circle and fixed disc results of integral type contractive self-mappings, which generalize many results of invariance and transformations in the literature.

Keywords

• fixed point
• fixed circle
• fixed disc
• Θc-contractions