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

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,...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-04, Vol.11 (8), p.1852
Main Authors: Huang, Huaping, Pal, Subhadip, Bera, Ashis, Dey, Lakshmi Kanta
Format: Article
Language:English
Subjects:
Analysis
Banach spaces
Boundary value problems
compact mapping
Convex functions
Food science
Hausdorff measure of noncompactness
initial value problem
Kannan-type equicontraction
Mappings (Mathematics)
Theorems
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11081852