Iterative Approximation for Mean Nonexpansive Mappings in Uniformly Convex Spaces with a Fractional Volterra Application

Muhammet Knefati; Vatan Karakaya

doi:10.32323/ujma.1784049

Iterative Approximation for Mean Nonexpansive Mappings in Uniformly Convex Spaces with a Fractional Volterra Application

Abstract

This paper investigates fixed point theory for mean nonexpansive mappings in $p$-uniformly convex metric spaces. It first establishes the existence of fixed points together with a demiclosedness principle in this setting. Building on these foundations, the two-step Karakaya iteration scheme is introduced, and a detailed convergence analysis is provided. In particular, both a $\Delta$-convergence theorem and a strong convergence theorem for mean nonexpansive mappings are proved. To illustrate the applicability of the results, new examples are constructed that clarify the scope of the assumptions. Furthermore, a numerical application to a nonlinear fractional Volterra integral equation within the framework of a $p$-uniformly convex metric space is presented. The existence of a Bochner solution is demonstrated and approximated using the Karakaya iteration scheme, with its numerical performance compared to that of the S-iteration and Thakur schemes.

Keywords

$\Delta$-convergence, Fixed points, Fractional Volterra, Mean nonexpansive mappings, Metric spaces, $p$-uniformly convex metric spaces

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Muhammet Knefati ^*
0000-0002-0075-8693
Türkiye

Vatan Karakaya
0000-0003-4637-3139
Türkiye

Early Pub Date

December 4, 2025

Publication Date

December 11, 2025

Submission Date

September 15, 2025

Acceptance Date

November 17, 2025

Published in Issue

Year 2025 Volume: 8 Number: 4

DOI

https://doi.org/10.32323/ujma.1784049

IZ

https://izlik.org/JA62HG63NR

APA

Knefati, M., & Karakaya, V. (2025). Iterative Approximation for Mean Nonexpansive Mappings in Uniformly Convex Spaces with a Fractional Volterra Application. Universal Journal of Mathematics and Applications, 8(4), 199-210. https://doi.org/10.32323/ujma.1784049

AMA

1.Knefati M, Karakaya V. Iterative Approximation for Mean Nonexpansive Mappings in Uniformly Convex Spaces with a Fractional Volterra Application. Univ. J. Math. Appl. 2025;8(4):199-210. doi:10.32323/ujma.1784049

Chicago

Knefati, Muhammet, and Vatan Karakaya. 2025. “Iterative Approximation for Mean Nonexpansive Mappings in Uniformly Convex Spaces With a Fractional Volterra Application”. Universal Journal of Mathematics and Applications 8 (4): 199-210. https://doi.org/10.32323/ujma.1784049.

EndNote

Knefati M, Karakaya V (December 1, 2025) Iterative Approximation for Mean Nonexpansive Mappings in Uniformly Convex Spaces with a Fractional Volterra Application. Universal Journal of Mathematics and Applications 8 4 199–210.

IEEE

[1]M. Knefati and V. Karakaya, “Iterative Approximation for Mean Nonexpansive Mappings in Uniformly Convex Spaces with a Fractional Volterra Application”, Univ. J. Math. Appl., vol. 8, no. 4, pp. 199–210, Dec. 2025, doi: 10.32323/ujma.1784049.

ISNAD

Knefati, Muhammet - Karakaya, Vatan. “Iterative Approximation for Mean Nonexpansive Mappings in Uniformly Convex Spaces With a Fractional Volterra Application”. Universal Journal of Mathematics and Applications 8/4 (December 1, 2025): 199-210. https://doi.org/10.32323/ujma.1784049.

JAMA

1.Knefati M, Karakaya V. Iterative Approximation for Mean Nonexpansive Mappings in Uniformly Convex Spaces with a Fractional Volterra Application. Univ. J. Math. Appl. 2025;8:199–210.

MLA

Knefati, Muhammet, and Vatan Karakaya. “Iterative Approximation for Mean Nonexpansive Mappings in Uniformly Convex Spaces With a Fractional Volterra Application”. Universal Journal of Mathematics and Applications, vol. 8, no. 4, Dec. 2025, pp. 199-10, doi:10.32323/ujma.1784049.

Vancouver

1.Muhammet Knefati, Vatan Karakaya. Iterative Approximation for Mean Nonexpansive Mappings in Uniformly Convex Spaces with a Fractional Volterra Application. Univ. J. Math. Appl. 2025 Dec. 1;8(4):199-210. doi:10.32323/ujma.1784049