0000000000026347

AUTHOR

Moosa Gabeleh

0000-0001-5439-1631

showing 4 related works from this author

Cyclic (noncyclic) phi-condensing operator and its application to a system of differential equations

2019

We establish a best proximity pair theorem for noncyclic φ-condensing operators in strictly convex Banach spaces by using a measure of noncompactness. We also obtain a counterpart result for cyclic φ-condensing operators in Banach spaces to guarantee the existence of best proximity points, and so, an extension of Darbo’s fixed point theorem will be concluded. As an application of our results, we study the existence of a global optimal solution for a system of ordinary differential equations.

Pure mathematicsnoncyclic φ-condensing operatorDifferential equationApplied Mathematics010102 general mathematicsBanach spaceRegular polygonFixed-point theoremlcsh:QA299.6-433Extension (predicate logic)lcsh:Analysis01 natural sciencesMeasure (mathematics)Noncyclic ϕ-condensing operator010101 applied mathematicsstrictly convex Banach spaceOperator (computer programming)Settore MAT/05 - Analisi Matematicabest proximity pairOrdinary differential equationordinary differential equations0101 mathematicsAnalysisOrdinary differential equationMathematicsNonlinear Analysis
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A note on best proximity point theory using proximal contractions

2018

In this paper, a reduction technique is used to show that some recent results on the existence of best proximity points for various classes of proximal contractions can be concluded from the corresponding results in fixed point theory.

021103 operations researchApplied MathematicsMathematical analysisBest proximity point0211 other engineering and technologiesproximal contractionfood and beveragesFixed-point theorem02 engineering and technologyFixed point01 natural sciencesPoint theory010101 applied mathematicsProximal contractionReduction (complexity)fixed pointModeling and SimulationGeometry and Topology0101 mathematicsMathematics
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A New Extension of Darbo's Fixed Point Theorem Using Relatively Meir-Keeler Condensing Operators

2018

We consider relatively Meir–Keeler condensing operators to study the existence of best proximity points (pairs) by using the notion of measure of noncompactness, and extend a result of Aghajani et al. [‘Fixed point theorems for Meir–Keeler condensing operators via measure of noncompactness’, Acta Math. Sci. Ser. B35 (2015), 552–566]. As an application of our main result, we investigate the existence of an optimal solution for a system of integrodifferential equations.

Pure mathematicsGeneral Mathematics010102 general mathematicsFixed-point theoremExtension (predicate logic)01 natural sciencesMeasure (mathematics)010101 applied mathematicsstrictly convex Banach spaceoptimal solutionProximity pointSettore MAT/05 - Analisi MatematicaPoint (geometry)relatively Meir-Keeler condensing operator0101 mathematicsMathematics
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A New Approach to the Generalization of Darbo’s Fixed Point Problem by Using Simulation Functions with Application to Integral Equations

2019

We investigate the existence of fixed points of self-mappings via simulation functions and measure of noncompactness. We use different classes of additional functions to get some general contractive inequalities. As an application of our main conclusions, we survey the existence of a solution for a class of integral equations under some new conditions. An example will be given to support our results.

Class (set theory)Mathematics (miscellaneous)Fixed point problemSettore MAT/05 - Analisi MatematicaGeneralizationApplied MathematicsMeasure (physics)Applied mathematicsFixed pointIntegral equationFixed point measure of noncompactness simulation function integral equation.MathematicsResults in Mathematics
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