Estimating Fixed Points via New Iterative Scheme with an Application. (4th March 2022)

• Record Type: Journal Article
• Authors: Jubair, Mohd; Ali, Javid; Kumar, Santosh
• Other Names: Fulga Andreea Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-03-04
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/3740809
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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.