On the Extended Version of Krasnoselśkiĭ’s Theorem for Kannan-Type Equicontractive Mappings

Huaping Huang (), Subhadip Pal, Ashis Bera and Lakshmi Kanta Dey
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Huaping Huang: School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404020, China
Subhadip Pal: Department of Mathematics, National Institute of Technology Durgapur, Durgapur 713209, India
Ashis Bera: Department of Mathematics, School of Advanced Sciences, VIT Chennai, Chennai 600127, India
Lakshmi Kanta Dey: Department of Mathematics, National Institute of Technology Durgapur, Durgapur 713209, India

Mathematics, 2023, vol. 11, issue 8, 1-12

Abstract: The purpose of the paper is to establish a sufficient condition for the existence of a solution to the equation T ( u , C ( u ) ) = u using Kannan-type equicontractive mappings, T : A × C ( A ) ¯ → Y , where C is a compact mapping, A is a bounded, closed and convex subset of a Banach space Y . To achieve this objective, the authors have presented Sadovskii’s theorem, which utilizes the measure of noncompactness. The relevance of the obtained results has been illustrated through the consideration of various initial value problems.

Keywords: Hausdorff measure of noncompactness; compact mapping; Kannan-type equicontraction; initial value problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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