Graphical approach to the study of fixed point results involving hybrid contractions

Abstract

In this work, a new class of general contractive mappings, with the name Jaggi-Suzuki-type hybrid (K-α-ϕ)-contractive mapping is discussed in metric space equipped with a graph and new criteria for which the mapping is a Picard operator are studied. The superiority of this type of contractive mapping lies in the fact that its contractive inequality can be fixed in different ways, depending on the specified constants. Substantial illustrations are furnished to validate the axioms of our obtained ideas and to show their difference from the existing concepts. Supplementarily, some corollaries which collapse our obtained notion to recently propounded results in the literature are brought out and analysed.

Keywords

• Metric space
• Fixed point
• Jaggi-Suzuki-type contractive mapping
• Hybrid contractive mapping
• Connected graph
• Picard operator