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Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

A fixed-point algorithm of e-enriched non-expansive mappings with an application

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pp. 1389–1398Vol. 29Issue 5-AMay 2026DOI: 10.47974/JIM-2597XML
Received:
01 Jan 2026
Published Online:
27 Jun 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2597
Pages:
1389–1398

Abstract

This work introduces a four-step iterative scheme for approximating fixed points of E-enriched nonexpansive mappings in uniformly convex Banach spaces. Theoretical analysis establishes a strong convergence under suitable assumptions on the mapping or the underlying space. To demonstrate its practical relevance, the scheme is applied to an image restoration problem formulated within a fixed-point framework. The numerical results show stable reconstructions with enhanced PSNR and SNR values, indicating superior performance in handling inverse imaging tasks. These findings underline both the theoretical strength and the computational efficiency of the proposed approach.

Keywords

Subject Classifications

47H0947H1054H25

References

[1] K. H. Alam, Y. Rohen, and A. Tomar, “α, F)-Geraghty-type generalized F-contractions on non-Archimedean fuzzy metric-unlike spaces,” Demonstratio Mathematica, vol. 57, no. 1, Art. no. 20240046, pp. 1–15 (2024), doi: 10.1515/dema.
[2] S. Banach, “On operations in abstract sets and their applications to integral equations,” Fundamenta Mathematicae, vol. 3, pp. 133–18 (1922).
[3] W. A. Kirk, “A fixed-point theorem for mappings which do not increase distances,” American Mathematical Monthly, vol. 72, no. 9, pp. 1004–1006 (1965).
[4] D. Göhde, “On the Principle of Contractive Mappings,” Mathematical News, vol. 30, pp. 251–258 (1965).
[5] F. E. Browder, “Nonexpansive nonlinear operators in a Banach space,” in Proceedings of the National Academy of Sciences USA, pp. 1041–1044 (1965).
[6] V. Berinde, “Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces,” Carpathian Journal of Mathematics, vol. 35, pp. 293–304 (2019).
[7] V. Berinde, “Approximating fixed points of enriched nonexpansive mappings in Banach spaces by using a retraction displacement condition,” Carpathian Journal of Mathematics, vol. 36, no. 1, pp. 27–34 (2020).
[8] W. R. Mann, “Mean value methods in iteration,” Proceedings of the American Mathematical Society, vol. 4, no. 3, pp. 506–510 (1953).
[9] S. Ishikawa, “Fixed points by a new iteration method,” Proceedings of the American Mathematical Society, vol. 44, no. 1, pp. 147–150 (1974).
[10] R. P. Agarwal, D. O’Regan, and D. R. Sahu, “Iterative construction of fixed points of nearly asymptotically nonexpansive mappings,” J. Nonlinear Convex Anal., vol. 8, no. 1, pp. 61–79 (2007).
[11] M. A. Noor, “New approximation schemes for general variational inequalities,” J. Math. Anal. Appl., vol. 251, no. 1, pp. 217–229 (2000).
[12] K. Ullah and M. Arshad, “On different results for new three-step iteration process in Banach spaces,” Springer Plus, vol. 5, pp. 1–15 (2016).
[13] B. S. Thakur, D. Thakur, and M. Postolache, “A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings,” Appl. Math. Comput., vol. 275, pp. 147–155 (2016).
[14] H. Piri, B. Daraby, S. Rahrovi, and M. Ghasemi, “Approximating fixed points of generalized nonexpansive mappings in Banach spaces by new faster iteration process,” Numer. Algorithms, vol. 81, pp. 1129–1148 (2019).
[15] J. Ali and F. Ali, “A new iterative scheme for approximating fixed points with an application to delay differential equations,” Journal of Nonlinear Convex Analysis, vol. 21, pp. 2151–2163 (2020).
[16] D. Ali, S. Ali, P.-C. D., T. Antoniu, A. A. Zaagan, and A. M. Mahnashi, “A quicker iteration method for approximating the fixed point of generalized α–Reich–Suzuki no expansive mappings with applications,” Fractal and Fractional, vol. 7, p. 790 (2023).
[17] D. P. Shukla and V. Tiwari, “Fixed point algorithms using iteration technique,” Journal of Interdisciplinary Mathematics, vol. 22, no. 4, pp. 581–591 (2019).
[18] C. J. Nweke and A. U. Udom, “Random fixed-point algorithms for the stochastic split common problem of firmly non-expansive operators,” Journal of Interdisciplinary Mathematics, vol. 25, no. 6, pp. 1713–1732 (2022).
[19] M. J. Mousa and S. S. Abed, “Results on stability for iterative procedure in a convex metric space,” in AIP Conference Proceedings, vol. 2834, Art. no. 080068, (2023).
[20] N. S. Taresh, S. S. Albundi, and S. S. Abed, “Convergence of iterative algorithms in CAT (0) spaces,” Iraqi Journal of Science, vol. 63, no. 1, pp. 233–240 (2022), doi: 10.24996/ijs.2022.63.1.24.
[21] S. S. Al-Bundi, “New Creation of Julia Sets and Some Properties,” Bulletin of the Paranaense Society of Mathematics, vol. 43, pp. 1–10 (2023), doi: 10.5269/bspm.63640.
[22] A. Cegielski, Iterative Methods for Fixed Point Problems in Hilbert Spaces, Lecture Notes in Mathematics, vol. 2057, Berlin/Heidelberg, Germany: Springer, pp. 298 (2012), doi:10.1007/978-3-642-30901-4.
[23] T. Suzuki, “Fixed point theorems and convergence theorems for some generalized no expansive mappings,” J. Math. Anal. Appl., vol. 340, no. 2, pp. 1088–1095 (2008).
[24] K. Ullah, J. Ahmad, M. Arshad, and Z. Ma, “Approximation of fixed points for enriched Suzuki no expansive mappings with an application in Hilbert spaces,” Axioms, vol. 11, no. 1, preprint no. 14, pp. 1–12 (2022), doi: 10.3390/axioms11010014.
[25] R. Shukla and R. Pant, “Some fixed-point results for enriched no expansive type mappings in Banach spaces,” Applied General Topology, vol. 23, no. 1, pp. 31–43 (2022).
[26] J. García-Falset, E. Llorens-Fuster, and T. Suzuki, “Fixed point theory for a class of generalized no expansive mappings,” J. Math. Anal. Appl., vol. 375, pp. 185–195 (2011).
[27] C. S. Wong, “Approximation to fixed points of generalized no expansive mappings,” Proceedings of the American Mathematical Society, vol. 54, pp. 93–97 (1976).
[28] J. Schu, “Weak and strong convergence to fixed points of asymptotically nonexpansive mappings,” Bull. Aust. Math. Soc., vol. 43, pp. 153–159 (1991).
[29] Wataru Takahashi, Nonlinear Functional Analysis: Fixed Point Theory and Its Applications. Yokohama, Japan: Yokohama Publishers (1997). 
[30] R. P. Agarwal, D. O’Regan, and D. R. Sahu, Fixed Point Theory for Lipschitzian-Type Mappings with Applications, vol. 6. New York, USA: Springer (2009). doi: 10.1007/978-0-387-75818-3.

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