Condensed Kannan-Type Maps and Their Efficiency Measures in Complete Metric Spaces
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Date
2025
Journal Title
Journal ISSN
Volume Title
Publisher
Kyungpook Mathematical Journal
Abstract
Recently, some studies introduced interpolative Kannan-type maps for solving
non-unique fixed-point problems. However, these studies do not offer a technique for determining
the fractional powers of the maps, which would be useful in approximating the fixed
points. This study uses two symmetry terms of the conventional Kannan contraction to
define a novel condensed Kannan-type contraction in complete metric spaces. By imposing
the condensed map on the Picard operator, we prove the existence of unique and non-unique
fixed points. We also define a criterion for selecting an appropriate real constant α suitable
for approximating the fixed points of the condensed map. We consider two practical and
numerical examples to show both the versatility and validity of the hypotheses of this study.
These results show that the class of condensed maps is strictly larger than the existing class
Kannan-type maps, ensure suitability for solving both unique and non-unique fixed points,
and do so with a better convergence rate.