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Year 2025, Volume: 13 Issue: 2, 233 - 240, 31.10.2025

Seyit Temir

Abstract

References

  • [1] M. Bas¸arır, A. S¸ ahin, On the strong and D-convergence of S-iteration process for generalized nonexpansive mappings on CAT(0) space, Thai J. Math., 12(3), 2014, 549-559.
  • [2] M. Bas¸arır, A. S¸ ahin, On the strong and D-convergence theorems for total asymptotically nonexpansive mappings on CAT(0) space. Carpathian Math. Publ., 5(2), 2013, 170-179.
  • [3] M. Bridson, A. Haefliger, Metric Spaces of Non-Positive Curvature, Springer-Verlag, Berlin, Heidelberg, 1999.
  • [4] F. Bruhat F, J. Tits, Groupes reductifs sur un corps local, I. Donnees radicielles valuees Inst Hautes Etudes Sci Publ Math., 41, 1972, 5-251, doi:10.1007/BF02715544.
  • [5] D. Burago, Y. Burago, S. Ivanov, A course in metric geometry, in: Graduate Studies in Math., vol. 33, Amer. Math. Soc., Providence, RI, 2001.
  • [6] D. Chand, Y. Rohen, N. Saleem, M. Aphane, A. Razzaque, S-Pata-type contraction: a new approach to fixed-point theory with an application, Journal of Inequalities and Applications, 2024:59, 1–16.
  • [7] S. Dhompongsa, B. Panyanak, On D-convergence theorems in CAT(0) spaces, Comput. Math. Appl., 56, 2008, 2572-2579.
  • [8] S. Dhompongsa, A. Kaewkhao, B. Panyanak, Lim’s theorems for multivalued mappings in CAT(0) spaces, J. Math. Anal. Appl. 312, 2005, 478-487.
  • [9] S. Dhompongsa, W. A. Kirk, B. Panyanak, Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal., 8, 2007, 35-45.
  • [10] S. Dhompongsa, W. A. Kirk, B. Sims, Fixed points of uniformly lipschitzian mappings, Nonlinear Anal. TMA, 65, 2006, 762-772.
  • [11] K. Fujiwara, K. Nagano, T. Shioya, Fixed point sets of parabolic isometries of CAT(0) spaces, Comment. Math. Helv., 81, 2006, 305-335.
  • [12] J.Garcia-Falset, E. Llorens-Fuster, T. Suzuki, Fixed point theory for a class of generalized nonexpansive mappings, J. Math. Anal. Appl., 375(1), 2011, 185-195.
  • [13] B. Iqbal, N. Saleem, M. Aphane, A. Razzaque, Fixed point results for I-Contractions in JS-generalized metric spaces with an application, PLoS ONE, 20(2), 2025, e0314493.
  • [14] N. Kadıoglu and I. Yıldırım, Approximating fixed points of nonexpansive mappings by faster iteration process, arXiv preprint, 2014, arXiv:1402.6530.
  • [15] E. Karapınar, Remarks on Suzuki (C)-condition, In Dynamical System and Methods; Springer: New York, NY, USA, 2012.
  • [16] M. N. A. Khan, M. Rashid, A. Kalsoom, N. Saleem, Madeeha, M. De La Sen, Approximation theorems for G -nonexpansive mappings in convex metric spaces by three step iterations, Alexandria Engineering Journal, 102, 2024, 1–9.
  • [17] W. A. Kirk, Geodesic geometry and fixed point theory, in: Seminar of Mathematical Analysis (Malaga/Seville, 2002/2003), in: Colecc. Abierta, vol. 64, Univ. Sevilla Secr. Publ., Seville, 2003, pp. 195-225.
  • [18] W. A. Kirk, Geodesic geometry and fixed point theory II, in: International Conference on Fixed Point Theory and Applications, Yokohama Publ., Yokohama, 2004, pp. 113-142.
  • [19] W. A. Kirk, Fixed point theorems in CAT(0) spaces and R-trees, Fixed Point Theory Appl., 2004, 309-316.
  • [20] W. A. Kirk, B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal. TMA, 68, 2008, 3689-3696.
  • [21] T. C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc., 60, 1976, 179-182.
  • [22] W. Phuengrattana, S. Suantai , On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval, J. Comput. Appl. Math., 235, 2011, 3006-3014.
  • [23] M. Rashid, N. Saleem, R. Bibi, R. George, Solution of integral equations using some multiple fixed point results in special kinds of distance spaces, Mathematics, 10, 2022, 4707.
  • [24] A. Razzaque, N. Saleem, I. K. Agwu, U. Ishtiaq, M. Aphane, Strong and weak convergence theorems for the split feasibility problem of (b;k)-enriched strict pseudocontractive mappings with an application in Hilbert spaces, Symmetry, 16, 2024, 546.
  • [25] A. Razzaque, I. K. Agwu, N. Saleem, D. I. Igbokwe, M. Aphane, Novel fixed point results for a class of enriched nonspreading mappings in real Banach spaces, AIMS Mathematics, 10(2), 2025, 3884–3909.
  • [26] N. Saleem, I. K. Agwu, U. Ishtiaq, S. Radenovic, Strong convergence theorems for finite family of enriched strictly pseudocontractive mappings and FT-enriched Lipschitizian mappings using a new modified mixed-type Ishikawa iteration scheme with error, Symmetry, 14, 2022, 1032.
  • [27] N. Saleem, K. Ullah, H. A. Nabwey, H. Bilal, S. Ullah, R. George, Fixed point approximation of operators satisfying (RCSC)—condition in CAT(0) spaces, Mathematics, 11, 2023, 4658.
  • [28] N. Saleem, B. Iqbal, F. Hasan, W. Shatanawi, Existence results for Wardowski-type convex contractions and the theory of iterated function systems, Symmetry, 15, 2023, 1162.
  • [29] N. Saleem, M. T. Raazzia, N. Hussain, A. Asiri, Geraghty-Pata-Suzuki-type proximal contractions and related coincidence best proximity point results, Symmetry, 15, 2023, 1572.
  • [30] A. S¸ ahin, O. Alagoz, On the approximation of fixed points for the class of mappings satisfying (CSC)-condition in Hadamard spaces, Carpathian Math. Publ., 15 (2), 2023, 495-506.
  • [31] A. S¸ ahin, M. Bas¸arır, On the strong and D-convergence of SP-iteration on CAT(0) space, J. Inequal. Appl., 311, 2013.
  • [32] H. F. Senter, W.G. Dotson Jr., Approximating fixed points of nonexpansive mappings, Proc. Am. Math. Soc., 44, 1974, 375-380.
  • [33] T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, Journal of Mathematical Analysis and Applications, 340(2), 2008, 1088-1095.
  • [34] S. Temir and O. Korkut, Approximating fixed point of the new SP*-iteration for generalized a-nonexpansive mappings in CAT(0) spaces, Journal of Nonlinear Analysis and Optimization: Theory and Applications, Vol. 12(2), 2021, pp.83-93.
  • [35] S. Temir, Convergence theorems for operators with property (E) in CAT(0) spaces, Journal of Nonlinear Analysis and Optimization: Theory and Applications, Vol. 15(2), 2024, 55-67.
  • [36] S. Temir, Approximating fixed points of the SP*-iteration for generalized nonexpansive mappings in CAT(0) spaces, Creat. Math. Inform., Volume 34(1), 2025, Pages 113-132.
  • [37] M. Zhou, N. Saleem, S. Bashir, Solution of fractional integral equations via fixed point results, Journal of Inequalities and Applications, 2022:148, 1–33.
  • [38] M. Zhou, G. Li, N. Saleem, O. Popescu, N. A. Secelean, Fixed point results for generalized convex orbital Lipschitz operators, Demonstratio Mathematica, 57, 2024, Article ID 20240082.

Fixed-Point Approximation of Operators Satisfying (HRSC)-condition in $CAT(0)$ Spaces

Year 2025, Volume: 13 Issue: 2, 233 - 240, 31.10.2025

Seyit Temir

Abstract

In this paper, we have established strong and $\Delta$-convergence results for the SP$^*$-iteration process applied to mappings satisfying the (HRSC)-condition in $CAT(0)$ spaces. Furthermore, a numerical example is provided to show the superiority of our results over existing ones and to illustrate the faster convergence of the SP$^*$-iteration process compared to several well-known iterative schemes.

Keywords

Fixed point iteration process mapping satisfying (HRSC) condition strong convergence $\Delta-$convergence $CAT(0)$ space

References

  • [1] M. Bas¸arır, A. S¸ ahin, On the strong and D-convergence of S-iteration process for generalized nonexpansive mappings on CAT(0) space, Thai J. Math., 12(3), 2014, 549-559.
  • [2] M. Bas¸arır, A. S¸ ahin, On the strong and D-convergence theorems for total asymptotically nonexpansive mappings on CAT(0) space. Carpathian Math. Publ., 5(2), 2013, 170-179.
  • [3] M. Bridson, A. Haefliger, Metric Spaces of Non-Positive Curvature, Springer-Verlag, Berlin, Heidelberg, 1999.
  • [4] F. Bruhat F, J. Tits, Groupes reductifs sur un corps local, I. Donnees radicielles valuees Inst Hautes Etudes Sci Publ Math., 41, 1972, 5-251, doi:10.1007/BF02715544.
  • [5] D. Burago, Y. Burago, S. Ivanov, A course in metric geometry, in: Graduate Studies in Math., vol. 33, Amer. Math. Soc., Providence, RI, 2001.
  • [6] D. Chand, Y. Rohen, N. Saleem, M. Aphane, A. Razzaque, S-Pata-type contraction: a new approach to fixed-point theory with an application, Journal of Inequalities and Applications, 2024:59, 1–16.
  • [7] S. Dhompongsa, B. Panyanak, On D-convergence theorems in CAT(0) spaces, Comput. Math. Appl., 56, 2008, 2572-2579.
  • [8] S. Dhompongsa, A. Kaewkhao, B. Panyanak, Lim’s theorems for multivalued mappings in CAT(0) spaces, J. Math. Anal. Appl. 312, 2005, 478-487.
  • [9] S. Dhompongsa, W. A. Kirk, B. Panyanak, Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal., 8, 2007, 35-45.
  • [10] S. Dhompongsa, W. A. Kirk, B. Sims, Fixed points of uniformly lipschitzian mappings, Nonlinear Anal. TMA, 65, 2006, 762-772.
  • [11] K. Fujiwara, K. Nagano, T. Shioya, Fixed point sets of parabolic isometries of CAT(0) spaces, Comment. Math. Helv., 81, 2006, 305-335.
  • [12] J.Garcia-Falset, E. Llorens-Fuster, T. Suzuki, Fixed point theory for a class of generalized nonexpansive mappings, J. Math. Anal. Appl., 375(1), 2011, 185-195.
  • [13] B. Iqbal, N. Saleem, M. Aphane, A. Razzaque, Fixed point results for I-Contractions in JS-generalized metric spaces with an application, PLoS ONE, 20(2), 2025, e0314493.
  • [14] N. Kadıoglu and I. Yıldırım, Approximating fixed points of nonexpansive mappings by faster iteration process, arXiv preprint, 2014, arXiv:1402.6530.
  • [15] E. Karapınar, Remarks on Suzuki (C)-condition, In Dynamical System and Methods; Springer: New York, NY, USA, 2012.
  • [16] M. N. A. Khan, M. Rashid, A. Kalsoom, N. Saleem, Madeeha, M. De La Sen, Approximation theorems for G -nonexpansive mappings in convex metric spaces by three step iterations, Alexandria Engineering Journal, 102, 2024, 1–9.
  • [17] W. A. Kirk, Geodesic geometry and fixed point theory, in: Seminar of Mathematical Analysis (Malaga/Seville, 2002/2003), in: Colecc. Abierta, vol. 64, Univ. Sevilla Secr. Publ., Seville, 2003, pp. 195-225.
  • [18] W. A. Kirk, Geodesic geometry and fixed point theory II, in: International Conference on Fixed Point Theory and Applications, Yokohama Publ., Yokohama, 2004, pp. 113-142.
  • [19] W. A. Kirk, Fixed point theorems in CAT(0) spaces and R-trees, Fixed Point Theory Appl., 2004, 309-316.
  • [20] W. A. Kirk, B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal. TMA, 68, 2008, 3689-3696.
  • [21] T. C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc., 60, 1976, 179-182.
  • [22] W. Phuengrattana, S. Suantai , On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval, J. Comput. Appl. Math., 235, 2011, 3006-3014.
  • [23] M. Rashid, N. Saleem, R. Bibi, R. George, Solution of integral equations using some multiple fixed point results in special kinds of distance spaces, Mathematics, 10, 2022, 4707.
  • [24] A. Razzaque, N. Saleem, I. K. Agwu, U. Ishtiaq, M. Aphane, Strong and weak convergence theorems for the split feasibility problem of (b;k)-enriched strict pseudocontractive mappings with an application in Hilbert spaces, Symmetry, 16, 2024, 546.
  • [25] A. Razzaque, I. K. Agwu, N. Saleem, D. I. Igbokwe, M. Aphane, Novel fixed point results for a class of enriched nonspreading mappings in real Banach spaces, AIMS Mathematics, 10(2), 2025, 3884–3909.
  • [26] N. Saleem, I. K. Agwu, U. Ishtiaq, S. Radenovic, Strong convergence theorems for finite family of enriched strictly pseudocontractive mappings and FT-enriched Lipschitizian mappings using a new modified mixed-type Ishikawa iteration scheme with error, Symmetry, 14, 2022, 1032.
  • [27] N. Saleem, K. Ullah, H. A. Nabwey, H. Bilal, S. Ullah, R. George, Fixed point approximation of operators satisfying (RCSC)—condition in CAT(0) spaces, Mathematics, 11, 2023, 4658.
  • [28] N. Saleem, B. Iqbal, F. Hasan, W. Shatanawi, Existence results for Wardowski-type convex contractions and the theory of iterated function systems, Symmetry, 15, 2023, 1162.
  • [29] N. Saleem, M. T. Raazzia, N. Hussain, A. Asiri, Geraghty-Pata-Suzuki-type proximal contractions and related coincidence best proximity point results, Symmetry, 15, 2023, 1572.
  • [30] A. S¸ ahin, O. Alagoz, On the approximation of fixed points for the class of mappings satisfying (CSC)-condition in Hadamard spaces, Carpathian Math. Publ., 15 (2), 2023, 495-506.
  • [31] A. S¸ ahin, M. Bas¸arır, On the strong and D-convergence of SP-iteration on CAT(0) space, J. Inequal. Appl., 311, 2013.
  • [32] H. F. Senter, W.G. Dotson Jr., Approximating fixed points of nonexpansive mappings, Proc. Am. Math. Soc., 44, 1974, 375-380.
  • [33] T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, Journal of Mathematical Analysis and Applications, 340(2), 2008, 1088-1095.
  • [34] S. Temir and O. Korkut, Approximating fixed point of the new SP*-iteration for generalized a-nonexpansive mappings in CAT(0) spaces, Journal of Nonlinear Analysis and Optimization: Theory and Applications, Vol. 12(2), 2021, pp.83-93.
  • [35] S. Temir, Convergence theorems for operators with property (E) in CAT(0) spaces, Journal of Nonlinear Analysis and Optimization: Theory and Applications, Vol. 15(2), 2024, 55-67.
  • [36] S. Temir, Approximating fixed points of the SP*-iteration for generalized nonexpansive mappings in CAT(0) spaces, Creat. Math. Inform., Volume 34(1), 2025, Pages 113-132.
  • [37] M. Zhou, N. Saleem, S. Bashir, Solution of fractional integral equations via fixed point results, Journal of Inequalities and Applications, 2022:148, 1–33.
  • [38] M. Zhou, G. Li, N. Saleem, O. Popescu, N. A. Secelean, Fixed point results for generalized convex orbital Lipschitz operators, Demonstratio Mathematica, 57, 2024, Article ID 20240082.
There are 38 citations in total.

Details

Primary Language English
Subjects Applied Mathematics (Other)
Journal Section Articles
Authors

Seyit Temir

Publication Date October 31, 2025
Submission Date April 28, 2025
Acceptance Date September 10, 2025
Published in Issue Year 2025 Volume: 13 Issue: 2

Cite

APA Temir, S. (2025). Fixed-Point Approximation of Operators Satisfying (HRSC)-condition in $CAT(0)$ Spaces. Konuralp Journal of Mathematics, 13(2), 233-240.
AMA Temir S. Fixed-Point Approximation of Operators Satisfying (HRSC)-condition in $CAT(0)$ Spaces. Konuralp J. Math. October 2025;13(2):233-240.
Chicago Temir, Seyit. “Fixed-Point Approximation of Operators Satisfying (HRSC)-Condition in $CAT(0)$ Spaces”. Konuralp Journal of Mathematics 13, no. 2 (October 2025): 233-40.
EndNote Temir S (October 1, 2025) Fixed-Point Approximation of Operators Satisfying (HRSC)-condition in $CAT(0)$ Spaces. Konuralp Journal of Mathematics 13 2 233–240.
IEEE S. Temir, “Fixed-Point Approximation of Operators Satisfying (HRSC)-condition in $CAT(0)$ Spaces”, Konuralp J. Math., vol. 13, no. 2, pp. 233–240, 2025.
ISNAD Temir, Seyit. “Fixed-Point Approximation of Operators Satisfying (HRSC)-Condition in $CAT(0)$ Spaces”. Konuralp Journal of Mathematics 13/2 (October2025), 233-240.
JAMA Temir S. Fixed-Point Approximation of Operators Satisfying (HRSC)-condition in $CAT(0)$ Spaces. Konuralp J. Math. 2025;13:233–240.
MLA Temir, Seyit. “Fixed-Point Approximation of Operators Satisfying (HRSC)-Condition in $CAT(0)$ Spaces”. Konuralp Journal of Mathematics, vol. 13, no. 2, 2025, pp. 233-40.
Vancouver Temir S. Fixed-Point Approximation of Operators Satisfying (HRSC)-condition in $CAT(0)$ Spaces. Konuralp J. Math. 2025;13(2):233-40.
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