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On generalization of Petryshyn's fixed point theorem and its application to the product of $ n $-nonlinear integral equations

Ateq Alsaadi, Manochehr Kazemi, Mohamed M. A. Metwali

2023AIMS Mathematics11 citationsDOIOpen Access PDF

Abstract

<abstract><p>Regarding the Hausdorff measure of noncompactness, we provide and demonstrate a generalization of Petryshyn's fixed point theorem in Banach algebras. Comparing this theorem to Schauder and Darbo's fixed point theorems, we can skip demonstrating closed, convex and compactness properties of the investigated operators. We employ our fixed point theorem to provide the existence findings for the product of $ n $-nonlinear integral equations in the Banach algebra of continuous functions $ C(I_a) $, which is a generalization of various types of integral equations in the literature. Lastly, a few specific instances and informative examples are provided. Our findings can successfully be extended to several Banach algebras, including $ AC, C^1 $ or $ BV $-spaces.</p></abstract>

Topics & Concepts

Fixed-point theoremMathematicsGeneralizationBrouwer fixed-point theoremPure mathematicsSchauder fixed point theoremHausdorff measureKakutani fixed-point theoremPicard–Lindelöf theoremFixed pointNonlinear systemProduct (mathematics)Hausdorff spaceFixed-point propertyDiscrete mathematicsMathematical analysisHausdorff dimensionPhysicsGeometryQuantum mechanicsNonlinear Differential Equations AnalysisAdvanced Banach Space TheoryFixed Point Theorems Analysis
On generalization of Petryshyn's fixed point theorem and its application to the product of $ n $-nonlinear integral equations | Litcius