Stability data dependency and errors estimation for a general iteration method

Hussain, Aftab; Ali, Danish; Karapınar, Erdal

doi:10.1016/j.aej.2020.10.002

Cited by 18 publications

(14 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With a view to locating fixed points of nonexpansive mappings, Mann [4], Ishikawa [5] and Halpern [6] introduced three basic iteration processes. In the same area we direct the reader to the recent works [7,8].…”

Section: Introductionmentioning

confidence: 99%

Convergence analysis of a novel iteration process with application to a fractional differential equation

et al. 2022

View full text Add to dashboard Cite

The objective of this article is to study a three-step iteration process in the framework of Banach spaces and to obtain convergence results for Suzuki generalized nonexpansive mappings. We also provide numerical examples that support our main results and illustrate the convergence behavior of the proposed process. Further, we present a data-dependence result that is also supported by a nontrivial numerical example. Finally, we discuss the solution of a nonlinear fractional differential equation by utilizing our results.

show abstract

Section: Introductionmentioning

confidence: 99%

Convergence analysis of a novel iteration process with application to a fractional differential equation

et al. 2022

View full text Add to dashboard Cite

show abstract

“…In recent years, many papers studied Mann [4] and Ishikawa [5] processes in various ways for single and multivalued contractive mappings. For more details in this direction, we refer the reader to [6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Convergence of Mann and Ishikawa Iterative Processes for Some Contractions in Convex Generalized Metric Space

Kouch

Mouline

2022

Abstract and Applied Analysis

View full text Add to dashboard Cite

show abstract

“…So, to overcome this kind of problem, several researchers constructed iterative schemes to approximate fixed points of mappings. A few of them are Picard-S [3], Thakur-New [4], and others [5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Estimating Fixed Points via New Iterative Scheme with an Application

Jubair

Ali

Kumar

2022

Journal of Function Spaces

View full text Add to dashboard Cite

In this paper, we introduce a new scheme and prove convergence results for nonexpansive mappings as well as for weak contractions in the frame of Banach spaces. Moreover, we prove analytically and numerically that the proposed scheme converges to a fixed point of a weak contraction faster than some known and leading schemes. Further, we prove that the new scheme is almost stable with respect to weak contraction. For supporting the main results, we give a couple of nontrivial numerical examples, and the visualization is shown by using the Matlab program. Finally, the solution of a nonlinear fractional differential equation is approximated by operating the main result of the paper.

show abstract

Stability data dependency and errors estimation for a general iteration method

Cited by 18 publications

References 22 publications

Convergence analysis of a novel iteration process with application to a fractional differential equation

Convergence analysis of a novel iteration process with application to a fractional differential equation

Convergence of Mann and Ishikawa Iterative Processes for Some Contractions in Convex Generalized Metric Space

Estimating Fixed Points via New Iterative Scheme with an Application

Contact Info

Product

Resources

About