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Dergiler / Eastern Anatolian Journal of Science / 2026 / Volume: 12 Issue: 1

Convergence Results for Mappings Satisfying the (HRSC)-Condition in Uniformly Convex Hyperbolic Spaces

Nazlı Kadıoğlu Karaca(Atatürk Üniversitesi, Fen Fakültesi, Matematik Bölümü)
Sayfa
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Yayın Tarihi
2026-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The results extend and complement several existing convergence theorems for generalized nonexpansive mappings.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we investigate fixed point approximation for mappings satisfying the Hardy-Rogers-Suzuki-type condition in uniformly convex hyperbolic spaces.
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Temel Bulgular & Veri:By using a modified M-iteration process, we establish Δ-convergence and strong convergence results under suitable assumptions.
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Sonuç & Katkı:The results extend and complement several existing convergence theorems for generalized nonexpansive mappings.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Fixed point · (HRSC)-condition · Generalized nonexpansive mapping

Abstract

In this paper, we investigate fixed point approximation for mappings satisfying the Hardy-Rogers-Suzuki-type condition in uniformly convex hyperbolic spaces. By using a modified M-iteration process, we establish Δ-convergence and strong convergence results under suitable assumptions. An example illustrating the applicability of the obtained results is presented. The results extend and complement several existing convergence theorems for generalized nonexpansive mappings.

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Bu Makaleye Atıf Yap

Karaca, N. K. (2026). Convergence Results for Mappings Satisfying the (HRSC)-Condition in Uniformly Convex Hyperbolic Spaces. Eastern Anatolian Journal of Science, Volume: 12 Issue: 1. https://ajindex.com/articles/1475614

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Kaynakça (29)

  1. ALAGOZ, O., GUNDUZ, B., AKBULUT, S. (2018). Numerical reckoning fixed points for Berinde mappings via a faster iteration process. Facta Univ. Ser. Math. Inform., 33, 295–305.
  2. ARIZA-RUIZ, D., LEUSTEAN, L., LOPEZ-ACEDO, G. (2014). Firmly nonexpansive mappings in classes of geodesic spaces. Trans. Am. Math. Soc, 366, 4299-4322.
  3. BANACH, S. (1922) Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta mathematicae, 3, 133-181.
  4. BROWDER, F. E. (1965) Nonexpansive nonlinear operators in a Banach space, Proceedings of the National Academy of Sciences of the United States of America, vol. 54, no. 4, pp. 1041–1044.
  5. CHATTERJEA, S. K. (1972). Fixed-point theorems,Comptes Rendus de l’Academie Bulgare des Sciences, 25, 727-730.
  6. CIRIC, L. B. (1974). A generalization of Banach principle, Proc. Amer. Math. Soc., 45, 267–273.
  7. DHOMPONGSA, S., PANYANAK, B. (2008 ).On D-convergence theorems in CAT(0) spaces, Comput. Math. Appl., 56, 2572-2579.
  8. GOEBEL, K. and KIRK, W. A. (1983). Iteration processes for nonexpansive mappings, Contemporary Mathematics, 21, 115–123.
  9. GOHDE, D. (1965). Zum prinzip der kontraktiven abbildung, Mathematische Nachrichten, 30, 3-4, 251–258.
  10. HARDY, G. E., ROGERS, T. D. (1973). A generalization of a fixed point theorem of Reich, Canad. Math. Bull., 16, 201–206.
  11. KANNAN, R. (1968). Some results on fixed points. Bull. Calcutta Math. Soc. 60, 71–76.
  12. KARAPINAR, E. (2012). Remarks on Suzuki (C)-condition. In Dynamical System and Methods; Springer: New York, NY, USA.
  13. KHAN, S. H.; ABBAS, M. (2011). Strong and Δ-convergence of some iterative schemes in CAT(0) spaces. Computers & Mathematics with Applications, 61, 109–116.
  14. KHAN, A. R., FUKHAR-UD DIN, H. KHAN, M. A. A. (. 2012). An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces. Fixed Point Theory Appl. 2012, 12.
  15. KIRK, W. A. (1965). A fixed point theorem for mappings which do not increase distances, The American mathematical monthly, 72, 9, 1004–1006.
  16. KIRK, W. A., Panyanak, B., (2008). A concept of convergence in geodesic spaces, Nonlinear Anal. TMA, 68, 3689-3696.
  17. KOHLENBACH, U. (2005). Some logical metatheorems with applications in functional analysis, Transactions of the American Mathematical Society, 357, 1, 89–128,.
  18. LEUSTEAN, L. (2010). Nonexpansive iterations in uniformly convex W-hyperbolic spaces, Nonlinear analysis and optimization I. Nonlinear analysis, 513, 193–209.
  19. REICH, S. (1971). Kannan’s fixed point theorem, Boll.Un. Mat. Ital., 4(4), 1–11.
  20. SALEEM, N., ULLAH, K., NABWEY, H. A., BILAL, H., ULLAH, S., GEORGE, R. (2023). Fixed-point approximation of operators satisfying (RCSC)-condition in CAT(0) spaces. Mathematics, 11(22), 4658.
  21. SENTER, H.F., DOTSON, W.G., Jr. (1974). Approximating fixed points of nonexpansive mappings. Proc. Am. Math. Soc., 44, 375-380.
  22. SHUKLA, R. (2022). Approximating Solutions of Optimization Problems via Fixed Point Techniques in Geodesic Spaces. Axioms, 11(10), 492.
  23. SHUKLA, R. and PANICKER, R. (2022). Approximating fixed points of enriched nonexpansive mappings in geodesic spaces. Journal of Function Spaces, 2022 (1), 6161839.
  24. SUZUKI, T. (2008). Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, Journal of Mathematical Analysis and Applications, 340(2), 1088-1095.
  25. SOSOV, E.N. (2004). On analogues of weak convergence in a special metric space. Izv. Vyss. Uchebnykh Zaved. Mat, 48, 84-89.
  26. TAKAHASHI, W. (1970). A convexity in metric space and nonexpansive mappings, I. In Kodai mathematical seminar reports, 22, 142-149.
  27. TEMIR, S. KORKUT, O. (2021). Approximating fixed points of the new SP*-iteration for generalized α-nonexpansive mappings in CAT(0) spaces. Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 12.2: 83-93.
  28. TEMIR, S. (2025). Fixed-Point Approximation of Operators Satisfying (HRSC)-condition in CAT(0) Spaces. Konuralp Journal of Mathematics, 13(2), 233-240.
  29. ULLAH, K., ARSHAD, M. (2018). Numerical reckoning fixed point for Suzuki’s generalized non-expansive mappings via new iteration process. Filomat, 32, 187–196.