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• W4280568045 abstract "In this manuscript, we propose a novel three - step iteration scheme called <math xmlns=http://www.w3.org/1998/Math/MathML id=M2> <mi mathvariant=fraktur>M</mi> </math> - iteration to approximate the invariant points for the class of weak contractions in the sense of Berinde and obtain that <math xmlns=http://www.w3.org/1998/Math/MathML id=M3> <mi mathvariant=fraktur>M</mi> </math> - iteration strongly converges to one and only one fixed point for Berinde mappings. Proving ‘almost - stability’ of <math xmlns=http://www.w3.org/1998/Math/MathML id=M4> <mi mathvariant=fraktur>M</mi> </math> - iteration, we compare the <math xmlns=http://www.w3.org/1998/Math/MathML id=M5> <mi mathvariant=fraktur>M</mi> </math> - iterative scheme with other chief iterative algorithms, namely. Picard, Mann, Ishikawa, Noor, S, normal-S, Abbas, Thakur, Varat, Ullah and <math xmlns=http://www.w3.org/1998/Math/MathML id=M6> <msup> <mrow> <mi>F</mi> </mrow> <mi>∗</mi> </msup> </math> and claim that the framed iterative procedure converges to the invariant points of weak contractions at faster rate than other vital algorithms. Some numerical illustrations are adduced to strengthen our claim. We further ascertain data dependency through <math xmlns=http://www.w3.org/1998/Math/MathML id=M7> <mi mathvariant=fraktur>M</mi> </math> - iteration. Finally, we establish the solution of Caputo type fractional differential equation as an application and exhibit that <math xmlns=http://www.w3.org/1998/Math/MathML id=M8> <mi mathvariant=fraktur>M</mi> </math> - fixed point procedure converges to the solution of a fractional differential equation. The obtained results are not only new but, also, extend the scope of previous findings." @default.
• W4280568045 created "2022-05-22" @default.
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• W4280568045 date "2022-05-14" @default.
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• W4280568045 title "Convergence and Stability of a Novel <math xmlns=http://www.w3.org/1998/Math/MathML id=M1> <mi mathvariant=fraktur>M</mi> </math>‐Iterative Algorithm with an Application" @default.
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• W4280568045 doi "https://doi.org/10.1155/2022/9327527" @default.
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