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The New Iterative Approximating of Endpoints of Multivalued Nonexpansive Mappings in Banach Spaces

Yıl 2022, Cilt: 5 Sayı: 2, 64 - 68, 30.06.2022
https://doi.org/10.32323/ujma.1004517

Öz

The purpose of this paper is to introduce the new iteration process to approximate endpoints of multivalued nonexpansive mappings in Banach space. We prove weak and strong convergence theorems of proposed iterative scheme under some suitable assumptions in the framework of a uniformly convex Banach space.

Kaynakça

  • [1] J. P. Aubin, J. Siegel, Fixed points and stationary points of dissipative multivalued maps, Proc. Am. Math. Soc., 78(3) (1980), 391-398.
  • [2] H. W. Corley, Some hybrid fixed point theorems related to optimization, J. Math. Anal. Appl., 120(2) (1986), 528-532.
  • [3] B. Panyanak, Approximating endpoints of multi-valued nonexpansive mappings in Banach spaces, J. Fixed Point Theory Appl., 20(2) (2018), Article ID: 77, 8 pages, doi:10.1007/s11784-018-0564-z.
  • [4] T. Laokul, Browder’s convergence theorem for multivalued mappings in Banach spaces without the endpoint condition, Abstract and Applied Analysis, 2020 (2020), Article ID: 6150398, 7 pages, doi:10.1155/2020/6150398.
  • [5] T. Abdeljawad, K. Ullah, J. Ahmad, N. Mlaiki, Iterative approximation of endpoints for multivalued mappings in Banach spaces, Journal of Function Spaces, 2020 (2020), Article ID: 2179059, doi:10.1155/2020/2179059.
  • [6] K. Ullah, J. Ahmad, M. Arshad, M. Sen, M. S. U. Khan, Approximating stationary point of multivalued generalized nonexpansive mappings in Banach spaces, Advances in Mathematical Physics, 2020 (2020), Article ID: 9086078, 6 pages, doi:10.1155/2020/9086078.
  • [7] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73(4)(1967), 591-597.
  • [8] H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Analysis: Theory, Methods & Applications, 16(12) (1991), 1127-1138, doi:10.1016/0362-546X(91)90200-K.
  • [9] B. Panyanak, Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Comp. Math. Appl., 54(6) (2007), 872-877 doi:10.1016/j.camwa.2007.03.012.
  • [10] B. Panyanak, Endpoints of multivalued nonexpansive mappings in geodesic spaces, Fixed Point Theory Appl., 2015, Article ID: 147, 11 pages, doi:10.1186/s13663-015-0398-y.
  • [11] B. Panyanak, The demiclosed principle for multi-valued nonexpansive mappings in Banach spaces. J. Nonlinear Convex Anal., 17(10) (2016), 2063-2070.
  • [12] P. Chuadchawna, A Farajzadeh, A. Kaewcharoen, Convergence theorems and approximating endpoints for multivalued Suzuki mappings in hyperbolics spaces, J. Comp. Anal. Appl., 28(5) (2020), 903-916.
Yıl 2022, Cilt: 5 Sayı: 2, 64 - 68, 30.06.2022
https://doi.org/10.32323/ujma.1004517

Öz

Kaynakça

  • [1] J. P. Aubin, J. Siegel, Fixed points and stationary points of dissipative multivalued maps, Proc. Am. Math. Soc., 78(3) (1980), 391-398.
  • [2] H. W. Corley, Some hybrid fixed point theorems related to optimization, J. Math. Anal. Appl., 120(2) (1986), 528-532.
  • [3] B. Panyanak, Approximating endpoints of multi-valued nonexpansive mappings in Banach spaces, J. Fixed Point Theory Appl., 20(2) (2018), Article ID: 77, 8 pages, doi:10.1007/s11784-018-0564-z.
  • [4] T. Laokul, Browder’s convergence theorem for multivalued mappings in Banach spaces without the endpoint condition, Abstract and Applied Analysis, 2020 (2020), Article ID: 6150398, 7 pages, doi:10.1155/2020/6150398.
  • [5] T. Abdeljawad, K. Ullah, J. Ahmad, N. Mlaiki, Iterative approximation of endpoints for multivalued mappings in Banach spaces, Journal of Function Spaces, 2020 (2020), Article ID: 2179059, doi:10.1155/2020/2179059.
  • [6] K. Ullah, J. Ahmad, M. Arshad, M. Sen, M. S. U. Khan, Approximating stationary point of multivalued generalized nonexpansive mappings in Banach spaces, Advances in Mathematical Physics, 2020 (2020), Article ID: 9086078, 6 pages, doi:10.1155/2020/9086078.
  • [7] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73(4)(1967), 591-597.
  • [8] H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Analysis: Theory, Methods & Applications, 16(12) (1991), 1127-1138, doi:10.1016/0362-546X(91)90200-K.
  • [9] B. Panyanak, Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Comp. Math. Appl., 54(6) (2007), 872-877 doi:10.1016/j.camwa.2007.03.012.
  • [10] B. Panyanak, Endpoints of multivalued nonexpansive mappings in geodesic spaces, Fixed Point Theory Appl., 2015, Article ID: 147, 11 pages, doi:10.1186/s13663-015-0398-y.
  • [11] B. Panyanak, The demiclosed principle for multi-valued nonexpansive mappings in Banach spaces. J. Nonlinear Convex Anal., 17(10) (2016), 2063-2070.
  • [12] P. Chuadchawna, A Farajzadeh, A. Kaewcharoen, Convergence theorems and approximating endpoints for multivalued Suzuki mappings in hyperbolics spaces, J. Comp. Anal. Appl., 28(5) (2020), 903-916.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Makbule Kaplan 0000-0002-7962-702X

Yayımlanma Tarihi 30 Haziran 2022
Gönderilme Tarihi 4 Ekim 2021
Kabul Tarihi 1 Mart 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 2

Kaynak Göster

APA Kaplan, M. (2022). The New Iterative Approximating of Endpoints of Multivalued Nonexpansive Mappings in Banach Spaces. Universal Journal of Mathematics and Applications, 5(2), 64-68. https://doi.org/10.32323/ujma.1004517
AMA Kaplan M. The New Iterative Approximating of Endpoints of Multivalued Nonexpansive Mappings in Banach Spaces. Univ. J. Math. Appl. Haziran 2022;5(2):64-68. doi:10.32323/ujma.1004517
Chicago Kaplan, Makbule. “The New Iterative Approximating of Endpoints of Multivalued Nonexpansive Mappings in Banach Spaces”. Universal Journal of Mathematics and Applications 5, sy. 2 (Haziran 2022): 64-68. https://doi.org/10.32323/ujma.1004517.
EndNote Kaplan M (01 Haziran 2022) The New Iterative Approximating of Endpoints of Multivalued Nonexpansive Mappings in Banach Spaces. Universal Journal of Mathematics and Applications 5 2 64–68.
IEEE M. Kaplan, “The New Iterative Approximating of Endpoints of Multivalued Nonexpansive Mappings in Banach Spaces”, Univ. J. Math. Appl., c. 5, sy. 2, ss. 64–68, 2022, doi: 10.32323/ujma.1004517.
ISNAD Kaplan, Makbule. “The New Iterative Approximating of Endpoints of Multivalued Nonexpansive Mappings in Banach Spaces”. Universal Journal of Mathematics and Applications 5/2 (Haziran 2022), 64-68. https://doi.org/10.32323/ujma.1004517.
JAMA Kaplan M. The New Iterative Approximating of Endpoints of Multivalued Nonexpansive Mappings in Banach Spaces. Univ. J. Math. Appl. 2022;5:64–68.
MLA Kaplan, Makbule. “The New Iterative Approximating of Endpoints of Multivalued Nonexpansive Mappings in Banach Spaces”. Universal Journal of Mathematics and Applications, c. 5, sy. 2, 2022, ss. 64-68, doi:10.32323/ujma.1004517.
Vancouver Kaplan M. The New Iterative Approximating of Endpoints of Multivalued Nonexpansive Mappings in Banach Spaces. Univ. J. Math. Appl. 2022;5(2):64-8.

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