Convergence Analysis of Picard Thakur Hybrid Iterative Scheme for  α-Nonexpansive Mappings in Uniformly Convex Banach Spaces

Convergence of Iterative Schemes in Uniformly Convex Banach Spaces.

  • Authors

    • Khushdil Ahmad Department of Mathematics, Government College University, Katechery Road, Lahore 54000, Pakistan
    • Khurram Shabbir Department of Mathematics, Government College University, Katchery Road 54000, Lahore
    • Nazia Nazar Department of Mathematics, Government College University, Katchery Road 54000, Lahore
    2024-04-28
    https://doi.org/10.14419/xtneae93
  • Banach space; Fixed Point; Generalized $\alpha$-Nonexpansive Mapping; Numerical Example; Picard-Thakur hybrid iterative scheme

  • Abstract

    In this study, we investigate the convergence behavior of fixed points for generalized  α-nonexpansive mappings using the Picard-Thakur hybrid iterative scheme. We obtain weak and strong convergence results for generalized  α-nonexpansive mappings in a uniformly convex Banach space. Numerically, we demonstrate that the Picard-Thakur hybrid iterative scheme converges more rapidly than other well-known schemes. Additionally, we present findings on data dependence and provide a numerical example to illustrate the concept. The obtained results are expanded and generalized to be consistent with relevant findings in the existing literature.

         

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  • How to Cite

    Ahmad, K., Shabbir, K., & Nazar, N. (2024). Convergence Analysis of Picard Thakur Hybrid Iterative Scheme for  α-Nonexpansive Mappings in Uniformly Convex Banach Spaces: Convergence of Iterative Schemes in Uniformly Convex Banach Spaces. International Journal of Applied Mathematical Research, 13(1), 34-48. https://doi.org/10.14419/xtneae93