Research Article
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Year 2023, Volume: 11 Issue: 2, 223 - 228, 25.12.2023
https://doi.org/10.51354/mjen.1361003

Abstract

References

  • [1] Abbas, M., Nazir, T., A new faster iteration process applied to constrained minimizationand feasibility problems, Matematicki Vesnik, 66(2) (2014), 223–234.
  • [2] Adeyemi, T. A., Akutsah, F., Mebawondu, A. A., Adewole, M. O., and Narain, O. K., The existence of a solution of the nonlinear integral equation via the fixed point approach, Adv. Math. Sci. J., 10 (2021), 2977–2998.
  • [3] Ali, J., Ali, F., Kumar, P.: Approximation of fixed points for Suzuki’s generalized non-expansive mappings. Mathematics. 7(6), 522 (2019)
  • [4] Aoyama, K., Kohsaka, F.: Fixed point theorem for 𝛼- nonexpansive mappings in Banach spaces. Nonlinear Anal. 74(13), 4387–4391 (2011)
  • [5] Bauschke, H. H. and Combettes, P. L., Convex analysis and monotone operator theory in Hilbert spaces, Springer, New York, 2011
  • [6] Browder, F. E., Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. USA.,54 (1965), 1041–1044.
  • [7] Chuadchawna, P., Farajzadeh, A., Kaewcharoen, A., Fixedpoint approximation of generalized nonexpansive mappings via generalized M-iteration in hyperbolic spaces, Int. J. Math. Sci., 2020 (2020), 1-8.
  • [8] Dhompongsa, S. and Panyanak, B., On 4-convergence theorems in CAT(0) spaces, Comput. Math. Appl., 56 (2008), No. 10, 2572–2579
  • [9] Goebel, K. and Kirk, W. A., Iteration processes for nonexpansive mappings, in Singh, S. P., Thomeier, S. and Watson, B., (Eds), Topological Methods in Nonlinear Functional Analysis, Contemp. Math., vol. 21, Am. Math. Soc., Providence, 1983, 115–123
  • [10] Goebel, K. and Reich, S., Uniform convexity, hyperbolic geometry and nonexpansive mappings, Marcel Dekker, New York, 1984
  • [11] Khan, A. R., Fukhar-ud-din, H. and Khan, M. A. A., An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces, Fixed Point Theory Appl., 2012, (2012), No. 54, 1–12
  • [12] Kirk, W. A., Panyanak, B., A concept of convergence in geodesic spaces, Nonlinear Anal. Theory Methods Appl., Ser. A, Theory Methods, 68 (12) (2008), 3689–3696.
  • [13] Kohlenbach, U., Some logical metatheorems with applications in functional analysis, Trans. Am. Math. Soc., 357 (2005), No. 1, 89–128
  • [14] Leustean, L., Nonexpansive iterations in uniformly convex W-hyperbolic spaces, in: Leizarowitz, A., Mordukhovich, B. S., Shafrir, I. and Zaslavski, A. (Eds), Nonlinear Analysis and Optimization I: Nonlinear Analysis, Contemp. Math., vol. 513, Am. Math. Soc., 2010, 193–209
  • [15] Lim, T. C., Remarks on some fixed point theorems, Proc. Am. Math. Soc., 60 (1976), No. 1, 179–182
  • [16] Pandey, R., Pant, R., Rakocevic, V., Shukla, R.,: Approximating fixed points of a general class of nonexpansive mappings in Banach spaces with applications. Results Math. 74(1), Article No. 7 (2019)
  • [17] Reich, S. and Shafrir, I., Nonexpansive iterations in hyperbolic spaces, Nonlinear Anal., 15 (1990), No. 6, 537–558
  • [18] Shimizu, T. and Takahashi, W., Fixed points of multivalued mappings in certain convex metric spaces, Topol. Methods Nonlinear Anal., 8 (1996), No. 1, 197–203
  • [19] Suzuki, T., Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008), no. 2, 1088–1095.
  • [20] Sahin, A. and Basarir, M., “Some convergence results for nonexpansive mappings in uniformly convex hyperbolic spaces,” Creat. Math. Inform., vol. 26, no. 3, pp. 331–338, 2017.
  • [21] Takahashi, W., A convexity in metric spaces and nonexpansive mappings, Kodai Math. Semin. Rep., 22, (1970), No. 2, 142–149
  • [22] Uddin, I. and Imdad, M., On certain convergence of Siteration scheme in CAT(0) spaces, Kuwait J. Sci., 42 (2015), No. 2, 93–106
  • [23] Ullah, K., Ahmad, J., & Sen, M. D. L. (2020). On generalized nonexpansive maps in Banach spaces. Computation, 8(3), 61.

On approximating fixed points of a new class of generalized nonexpansive mappings in uniformly convex hyperbolic space

Year 2023, Volume: 11 Issue: 2, 223 - 228, 25.12.2023
https://doi.org/10.51354/mjen.1361003

Abstract

In this paper, we introduce the definition of a new class of generalized nonexpansive
mappings in hyperbolic space. Additionally, we construct the rewritten version of
the Mann iteration process in hyperbolic space. Then, using the iterative procedure
we established, we prove convergence theorems for 𝑎−𝑏−generalized nonexpansive
mappings in a uniformly convex hyperbolic space. Lastly, we offer a numerical
example to illustrate our findings.

References

  • [1] Abbas, M., Nazir, T., A new faster iteration process applied to constrained minimizationand feasibility problems, Matematicki Vesnik, 66(2) (2014), 223–234.
  • [2] Adeyemi, T. A., Akutsah, F., Mebawondu, A. A., Adewole, M. O., and Narain, O. K., The existence of a solution of the nonlinear integral equation via the fixed point approach, Adv. Math. Sci. J., 10 (2021), 2977–2998.
  • [3] Ali, J., Ali, F., Kumar, P.: Approximation of fixed points for Suzuki’s generalized non-expansive mappings. Mathematics. 7(6), 522 (2019)
  • [4] Aoyama, K., Kohsaka, F.: Fixed point theorem for 𝛼- nonexpansive mappings in Banach spaces. Nonlinear Anal. 74(13), 4387–4391 (2011)
  • [5] Bauschke, H. H. and Combettes, P. L., Convex analysis and monotone operator theory in Hilbert spaces, Springer, New York, 2011
  • [6] Browder, F. E., Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. USA.,54 (1965), 1041–1044.
  • [7] Chuadchawna, P., Farajzadeh, A., Kaewcharoen, A., Fixedpoint approximation of generalized nonexpansive mappings via generalized M-iteration in hyperbolic spaces, Int. J. Math. Sci., 2020 (2020), 1-8.
  • [8] Dhompongsa, S. and Panyanak, B., On 4-convergence theorems in CAT(0) spaces, Comput. Math. Appl., 56 (2008), No. 10, 2572–2579
  • [9] Goebel, K. and Kirk, W. A., Iteration processes for nonexpansive mappings, in Singh, S. P., Thomeier, S. and Watson, B., (Eds), Topological Methods in Nonlinear Functional Analysis, Contemp. Math., vol. 21, Am. Math. Soc., Providence, 1983, 115–123
  • [10] Goebel, K. and Reich, S., Uniform convexity, hyperbolic geometry and nonexpansive mappings, Marcel Dekker, New York, 1984
  • [11] Khan, A. R., Fukhar-ud-din, H. and Khan, M. A. A., An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces, Fixed Point Theory Appl., 2012, (2012), No. 54, 1–12
  • [12] Kirk, W. A., Panyanak, B., A concept of convergence in geodesic spaces, Nonlinear Anal. Theory Methods Appl., Ser. A, Theory Methods, 68 (12) (2008), 3689–3696.
  • [13] Kohlenbach, U., Some logical metatheorems with applications in functional analysis, Trans. Am. Math. Soc., 357 (2005), No. 1, 89–128
  • [14] Leustean, L., Nonexpansive iterations in uniformly convex W-hyperbolic spaces, in: Leizarowitz, A., Mordukhovich, B. S., Shafrir, I. and Zaslavski, A. (Eds), Nonlinear Analysis and Optimization I: Nonlinear Analysis, Contemp. Math., vol. 513, Am. Math. Soc., 2010, 193–209
  • [15] Lim, T. C., Remarks on some fixed point theorems, Proc. Am. Math. Soc., 60 (1976), No. 1, 179–182
  • [16] Pandey, R., Pant, R., Rakocevic, V., Shukla, R.,: Approximating fixed points of a general class of nonexpansive mappings in Banach spaces with applications. Results Math. 74(1), Article No. 7 (2019)
  • [17] Reich, S. and Shafrir, I., Nonexpansive iterations in hyperbolic spaces, Nonlinear Anal., 15 (1990), No. 6, 537–558
  • [18] Shimizu, T. and Takahashi, W., Fixed points of multivalued mappings in certain convex metric spaces, Topol. Methods Nonlinear Anal., 8 (1996), No. 1, 197–203
  • [19] Suzuki, T., Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008), no. 2, 1088–1095.
  • [20] Sahin, A. and Basarir, M., “Some convergence results for nonexpansive mappings in uniformly convex hyperbolic spaces,” Creat. Math. Inform., vol. 26, no. 3, pp. 331–338, 2017.
  • [21] Takahashi, W., A convexity in metric spaces and nonexpansive mappings, Kodai Math. Semin. Rep., 22, (1970), No. 2, 142–149
  • [22] Uddin, I. and Imdad, M., On certain convergence of Siteration scheme in CAT(0) spaces, Kuwait J. Sci., 42 (2015), No. 2, 93–106
  • [23] Ullah, K., Ahmad, J., & Sen, M. D. L. (2020). On generalized nonexpansive maps in Banach spaces. Computation, 8(3), 61.
There are 23 citations in total.

Details

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

Nazlı Kadıoğlu Karaca 0000-0002-6308-5879

Publication Date December 25, 2023
Published in Issue Year 2023 Volume: 11 Issue: 2

Cite

APA Kadıoğlu Karaca, N. (2023). On approximating fixed points of a new class of generalized nonexpansive mappings in uniformly convex hyperbolic space. MANAS Journal of Engineering, 11(2), 223-228. https://doi.org/10.51354/mjen.1361003
AMA Kadıoğlu Karaca N. On approximating fixed points of a new class of generalized nonexpansive mappings in uniformly convex hyperbolic space. MJEN. December 2023;11(2):223-228. doi:10.51354/mjen.1361003
Chicago Kadıoğlu Karaca, Nazlı. “On Approximating Fixed Points of a New Class of Generalized Nonexpansive Mappings in Uniformly Convex Hyperbolic Space”. MANAS Journal of Engineering 11, no. 2 (December 2023): 223-28. https://doi.org/10.51354/mjen.1361003.
EndNote Kadıoğlu Karaca N (December 1, 2023) On approximating fixed points of a new class of generalized nonexpansive mappings in uniformly convex hyperbolic space. MANAS Journal of Engineering 11 2 223–228.
IEEE N. Kadıoğlu Karaca, “On approximating fixed points of a new class of generalized nonexpansive mappings in uniformly convex hyperbolic space”, MJEN, vol. 11, no. 2, pp. 223–228, 2023, doi: 10.51354/mjen.1361003.
ISNAD Kadıoğlu Karaca, Nazlı. “On Approximating Fixed Points of a New Class of Generalized Nonexpansive Mappings in Uniformly Convex Hyperbolic Space”. MANAS Journal of Engineering 11/2 (December 2023), 223-228. https://doi.org/10.51354/mjen.1361003.
JAMA Kadıoğlu Karaca N. On approximating fixed points of a new class of generalized nonexpansive mappings in uniformly convex hyperbolic space. MJEN. 2023;11:223–228.
MLA Kadıoğlu Karaca, Nazlı. “On Approximating Fixed Points of a New Class of Generalized Nonexpansive Mappings in Uniformly Convex Hyperbolic Space”. MANAS Journal of Engineering, vol. 11, no. 2, 2023, pp. 223-8, doi:10.51354/mjen.1361003.
Vancouver Kadıoğlu Karaca N. On approximating fixed points of a new class of generalized nonexpansive mappings in uniformly convex hyperbolic space. MJEN. 2023;11(2):223-8.

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