Generalized Kannan Type Fixed Point Theorems in Equivalent Distance Spaces

Abstract

This paper develops new fixed-point theorems for operators in metric spaces equipped with $\mathcal{E}_{A,B}$-distances. We investigate families of mappings $\{\mathcal{T}^t\}$ satisfying a generalized Kannan-type condition and establish existence and uniqueness results under appropriate constraints on the operator parameters. Our framework extends classical fixed-point theory while preserving its broad applicability.

The $\mathcal{E}_{A,B}$-distance structure proves particularly effective for analyzing nonlinear operators in functional analysis. An illustrative examples demonstrate the verifiability and practical utility of our theoretical conditions.