On fixed-point approximations for a class of nonlinear mappings based on the JK iterative scheme with application

Junaid Ahmad; Kifayat Ullah; Hasanen A. Hammad; Reny George

doi:10.3934/math.2023694

On fixed-point approximations for a class of nonlinear mappings based on the JK iterative scheme with application

Junaid Ahmad, Kifayat Ullah, Hasanen A. Hammad, Reny George

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The goal of this manuscript is to introduce the JK iterative scheme for the numerical reckoning of fixed points in generalized contraction mappings. Also, weak and strong convergence results are investigated under this scheme in the setting of Banach spaces. Moreover, two numerical examples are given to illustrate that the JK iterative scheme is more effective than some other iterative schemes in the literature. Ultimately, as an application, the JK iterative scheme is applied to solve a discrete composite functional differential equation of the Volterra-Stieljes type.

Original language	English
Pages (from-to)	13663-13679
Number of pages	17
Journal	AIMS Mathematics
Volume	8
Issue number	6
DOIs	https://doi.org/10.3934/math.2023694
State	Published - 2023

Keywords

convergence results
fixed point technique
iteration scheme
nonexpansive mapping
uniformly convex Banach space

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10.3934/math.2023694

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abstract = "The goal of this manuscript is to introduce the JK iterative scheme for the numerical reckoning of fixed points in generalized contraction mappings. Also, weak and strong convergence results are investigated under this scheme in the setting of Banach spaces. Moreover, two numerical examples are given to illustrate that the JK iterative scheme is more effective than some other iterative schemes in the literature. Ultimately, as an application, the JK iterative scheme is applied to solve a discrete composite functional differential equation of the Volterra-Stieljes type.",

keywords = "convergence results, fixed point technique, iteration scheme, nonexpansive mapping, uniformly convex Banach space",

author = "Junaid Ahmad and Kifayat Ullah and Hammad, \{Hasanen A.\} and Reny George",

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AU - Hammad, Hasanen A.

AU - George, Reny

PY - 2023

Y1 - 2023

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AB - The goal of this manuscript is to introduce the JK iterative scheme for the numerical reckoning of fixed points in generalized contraction mappings. Also, weak and strong convergence results are investigated under this scheme in the setting of Banach spaces. Moreover, two numerical examples are given to illustrate that the JK iterative scheme is more effective than some other iterative schemes in the literature. Ultimately, as an application, the JK iterative scheme is applied to solve a discrete composite functional differential equation of the Volterra-Stieljes type.

KW - convergence results

KW - fixed point technique

KW - iteration scheme

KW - nonexpansive mapping

KW - uniformly convex Banach space

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IS - 6

ER -

On fixed-point approximations for a class of nonlinear mappings based on the JK iterative scheme with application

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Keywords

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