FIXED POINT THEOREMS OF CONDENSED KANNAN-TYPE CONTRACTION IN 𝒢-METRIC SPACES

Abstract

In this paper, we introduce the notion of condensed Kannan-type contraction in 𝒢-metric spaces. We establish and prove some xed point theorems of operators satisfying the condensed Kannan-type map. To evaluate the efficacy of this condition, we define a new criterion, called the α-measure, in 𝒢-metric spaces to seamlessly assess the eectiveness and dynamicity of the condensed map. We consider some practical examples to validate and demonstrate the dominance of the condensed map over some existing Kannan-type maps in 𝒢-metric spaces. The results obtained ensure suitability for solving unique and non-unique fixed points and suggest a framework for selecting an appropriate real constant α∈(0,1) for studying nonlinear operators.