Fixed-point theorems of F ⋆ − ( ψ , ϕ ) ${F}^{\star}- ( \psi,\phi )$ integral-type contractive conditions on 1 E $1_{E}$ -complete multiplicative partial cone metric spaces over Banach algebras and applications

Abstract In this paper, we introduce some user-friendly versions of integral-type fixed-point results and give some modifications of the classical Banach contraction principle by constructing a special type of contractive restrictions of integral forms for weak contraction mappings defined on 1 E $1...

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Bibliographic Details
Published in:Journal of inequalities and applications 2023-11, Vol.2023 (1), p.1-26
Main Authors: Nashat Faried, Sahar Mohamed Ali Abou Bakr, H. Abd El-Ghaffar, S. S. Solieman Almassri
Format: Article
Language:English
Subjects:
Fixed points
Integral-type inequalities
Multiplicative algebra cones
Multiplicative partial cone metric spaces over Banach algebras
Multiplicative segments
Online Access:Get full text
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Summary:Abstract In this paper, we introduce some user-friendly versions of integral-type fixed-point results and give some modifications of the classical Banach contraction principle by constructing a special type of contractive restrictions of integral forms for weak contraction mappings defined on 1 E $1_{E}$ -complete multiplicative partial cone metric spaces over Banach algebras and formulate some existence and uniqueness results regarding the fixed-point theorems using some integrative conditions. Moreover, we validate the significance our results and exploit them to find the unique solution of a fractional nonlinear differential equation of Caputo type, which complements some previously well-known generalizations found in the literature.
ISSN:1029-242X
DOI:10.1186/s13660-023-03056-3