Convergence of generalized Mann iteration scheme for some contractive mappings in convex G b- metric spaces with application

Abstract

In this research, novel results on the generalized Mann iteration scheme to the existence of fixed points of Kannan
contraction mappings, Chatterjea contraction mappings and Hardy - Rogers contraction mappings in the framework
of complete convex G b-metric spaces, where convexity is defined in the sense of Takahashi, are respectively
established and illustrated. These results individually improve upon a similar result that has been established for
Banach contraction mappings in the same setting. Additionally, the result for Kannan contraction mappings is
applied to obtain the solution of an integral equation