FIXED POINT THEOREMS OF CONDENSED KANNAN-TYPE CONTRACTION IN G-METRIC SPACES
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Date
2025-06-30
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Abstract
In this paper, we introduce the notion of condensed Kannan-type contraction in
G-metric spaces. We establish and prove some fixed point theorems of operators satisfying
the condensed Kannan-type map. To evaluate the efficacy of this condition, we de fine a new
criterion, called the alpha-measure, in G-metric spaces to seamlessly assess the effectiveness
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 alpha in (0; 1)
for studying nonlinear operators.