Fixed point theorems for enriched Kannan mappings in CAT(0) spaces

Abstract

We present enriched Kannan and enriched Bianchini mappings in the framework of unique geodesic spaces. For such mappings, we establish the existence and uniqueness of a fixed point in the setting of CAT(0) spaces and show that an appropriate Krasnoselskij scheme converges with certain rate to the fixed point. We proved some inclusion relations between enriched Kannan mapping and some applicable mappings such as strongly demicontractive mapping. Finally, we give an example in a nonlinear CAT(0) space and perform numerical experiments to support the theoretical results.