Modified Geraghty Contraction Involving Fixed Point Theorems

Abstract

In this paper, we introduced a α-ψ-Geraghty contraction and established fixed point results for α-admissible mappings with respect to η in complete metric spaces. In the comparison of Geraghty contraction our new modified α-ψ-Geraghty contraction is more stronger. The example is given to show the validity of our results. Our results generalize / improve several results existing in the literature.

Key words and phrases. Unique fixed point; admissible with respect to η; α-ψ-Geraghty contraction; Geraghty contraction.

2000 Mathematics Subject Classification. 46S40; 47H10; 54H25