FIXED POINT RESULTS FOR MIXED POWER-TYPE CONTRACTIONS ON COMPLETE METRIC SPACES

Abstract

We establish two new fixed point theorems for operators on complete metricspaces with bounded diameters. First, we prove a general result for mappings satisfying amixed power-type condition. Second, we present a significant generalization of Kannan-type contractions through a novel nonlinear condition involving both point distances and their images. These results unify and extend classical fixed point principles, including Banach contractions, and Kannan's theorem, while operating under natural diameter constraints.The theorems' broad applicability is demonstrated through connections to existing literature and potential applications in nonlinear analysis.