Hybrid fixed point theorems of graphic contractions with applications

Abstract

In this work, a family of hybrid contractions, termed Jaggi-type hybrid (ℵ-τ)-contractive mapping is proposed in metric space equipped with a graph and new conditions under which the mapping is a Picard operator are studied. The novel ideas proposed in this manuscript are exemplified to display the validity of the presented results and to show how they differ from the existing ones. Additionally, some corollaries which reduce our proposed notion to some recently announced concepts in the existing findings are indicated and examined. Finally, we study Ulam-type stability for the fixed point equations with hybrid contractions.

Keywords

• Fixed point
• Jaggi-type contractive mapping
• Hybrid contractive mapping
• Graphic contraction
• Picard operator
• Ulam stability