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New numerical scheme for solving integral equations via fixed point method using distinct <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo linebreak="badbreak">-</mml:mo> <mml:mi>F</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> -contractions

Sumati Kumari Panda, Thabet Abdeljawad, K. Kumara Swamy

2020Alexandria Engineering Journal26 citationsDOIOpen Access PDF

Abstract

In this paper, we introduce the notion of (ω-F)-contraction and presented fixed point results for such contractions. Thereafter, by using the technique of fixed point method, we propose a simple solution for a nonlinear integral equation. The effectiveness of this fixed point approach is illustrated by numerical example.

Topics & Concepts

Fixed pointMathematicsSimple (philosophy)Nonlinear systemApplied mathematicsScheme (mathematics)Fixed-point theoremContraction (grammar)Mathematical analysisPhysicsEpistemologyMedicineQuantum mechanicsPhilosophyInternal medicineFixed Point Theorems Analysis
New numerical scheme for solving integral equations via fixed point method using distinct <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo linebreak="badbreak">-</mml:mo> <mml:mi>F</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> -contractions | Litcius