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Approximation of fixed points for Garcia-Falset mappings in a uniformly convex Banach space

Yıl 2021, Cilt: 4 Sayı: 4, 200 - 206, 31.12.2021
https://doi.org/10.53006/rna.960564

Öz

The aim of this research is to introduce a novel iterative technique termed CC-iteration for identifying the fixed points of Garcia-Falset mappings. In uniformly convex Banach spaces, we establish both weak and strong convergence characteristics. Additionally, numerical examples of the iterative approach are presented in the form of a signal recovery application in a compressed sensing issue.

Destekleyen Kurum

Chiang Mai University

Proje Numarası

R000027527

Teşekkür

CMU Junior Research Fellowship Program

Kaynakça

  • [1] P. L. Combettes, V. R. Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Model. Simul. 4 (2005) 1168-1200.
  • [2] J. Duchi, S. Shalev-Shwartz, Y. Singer, T. Chandra, E?cient projections onto the l 1 -ball for learning in high dimensions, In: Proceedings of the 25th International Conference on Machine Learning, Helsinki, Finland. (2008) 272-279.
  • [3] J. Garci­a-Falset, E. Llorens-Fuster, T. Suzuki, Fixed point theory for a class of generalized nonexpansive mappings, J.Math. Anal. Appl. 375 (2011) 185-195.
  • [4] H. Iiduka, W. Takahashi, Strong convergence theorems for nonexpansive nonself-mappings and inverse-strongly-monotone mappings, J. Convex Anal. 11 (2004) 69-79.
  • [5] S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. 4(1) (1974) 147-150.
  • [6] W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953) 506-510.
  • [7] M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251(1) (2000) 217-229.
  • [8] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math.Soc. 73(4) (1967) 591-598.
  • [9] J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Aust. Math. Soc.43(1) (1991) 153-159.
  • [10] H. F. Senter, W. G. Dotson, Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 44 (1974)375-380.
  • [11] S. Suantai, Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings, J. Math.Anal. Appl. 311(2) (2005) 506-517.
  • [12] R. Suparatulatorn, P. Charoensawan, K. Poochinapan, Inertial self-adaptive algorithm for solving split feasible problems with applications to image restoration, Math. Methods Appl. Sci. 42(18) (2019) 7268-7284.
  • [13] R. Suparatulatorn, A. Khemphet, Tseng type methods for inclusion and fixed point problems with applications, Mathematics. 7(12) (2019) 1175.
  • [14] R. Suparatulatorn, A. Khemphet, P. Charoensawan, S. Suantai, N. Phudolsitthiphat, Generalized self-adaptive algorithm for solving split common fixed point problem and its application to image restoration problem, Int. J. Comput. Math.97(7) (2020) 1431-1443.
  • [15] T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal.Appl. 340(2) (2008) 1088-1095.
  • [16] B. S. Thakur, D. Thakur, M. Postolache, A new iteration scheme for approximating fixed points of nonexpansive mappings, Filomat. 30(10) (2016) 2711-2720.
  • [17] G. I. Usurelu, A. Bejenaru, M. Postolache, Operators with property (E) as concerns numerical analysis and visualization, Numer. Funct. Anal. Optim. 41(11) (2020) 1398-1419.
  • [18] P. Cholamjiak, W. Cholamjiak, Fixed point theorems for hybrid multivalued mappings in Hilbert spaces, J. Fixed Point Theory Appl. 18 (2016) 673-688.
  • [19] P. Cholamjiak, A. A. Abdou, Y. J. Cho, Proximal point algorithms involving fixed points of nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl. 2015 (2015) 227.
  • [20] S. Kesornprom, N. Pholasa, P. Cholamjiak, On the convergence analysis of the gradient-CQ algorithms for the split feasibility problem, Numerical Algorithms. 84(3) (2020) 997-1017.
  • [21] S. Kesornprom, P. Cholamjiak, Proximal type algorithms involving linesearch and inertial technique for split variational inclusion problem in hilbert spaces with applications, Optimization. 68(12) (2019) 2369-2395.
  • [22] S. Suantai, S. Kesornprom, P. Cholamjiak, A new hybrid CQ algorithm for the split feasibility problem in Hilbert spaces and its applications to compressed sensing, Mathematics. 7(9) (2019) 789.
  • [23] R. Suparatulatorn, P. Charoensawan, K. Poochinapan, S. Dangskul, An algorithm for the split feasible problem and image restoration, RACSAM. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. 115 (2021). https://doi.org/10.1007/s13398-020-00942-z.
  • [24] R. Suparatulatorn, P. Charoensawan, A. Khemphet, An inertial subgradient extragradient method of variational inequality problems involving quasi-nonexpansive operators with applications, Math. Methods Appl. Sci. (2021).https://doi.org/10.1002/mma.7576.
Yıl 2021, Cilt: 4 Sayı: 4, 200 - 206, 31.12.2021
https://doi.org/10.53006/rna.960564

Öz

Proje Numarası

R000027527

Kaynakça

  • [1] P. L. Combettes, V. R. Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Model. Simul. 4 (2005) 1168-1200.
  • [2] J. Duchi, S. Shalev-Shwartz, Y. Singer, T. Chandra, E?cient projections onto the l 1 -ball for learning in high dimensions, In: Proceedings of the 25th International Conference on Machine Learning, Helsinki, Finland. (2008) 272-279.
  • [3] J. Garci­a-Falset, E. Llorens-Fuster, T. Suzuki, Fixed point theory for a class of generalized nonexpansive mappings, J.Math. Anal. Appl. 375 (2011) 185-195.
  • [4] H. Iiduka, W. Takahashi, Strong convergence theorems for nonexpansive nonself-mappings and inverse-strongly-monotone mappings, J. Convex Anal. 11 (2004) 69-79.
  • [5] S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. 4(1) (1974) 147-150.
  • [6] W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953) 506-510.
  • [7] M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251(1) (2000) 217-229.
  • [8] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math.Soc. 73(4) (1967) 591-598.
  • [9] J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Aust. Math. Soc.43(1) (1991) 153-159.
  • [10] H. F. Senter, W. G. Dotson, Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 44 (1974)375-380.
  • [11] S. Suantai, Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings, J. Math.Anal. Appl. 311(2) (2005) 506-517.
  • [12] R. Suparatulatorn, P. Charoensawan, K. Poochinapan, Inertial self-adaptive algorithm for solving split feasible problems with applications to image restoration, Math. Methods Appl. Sci. 42(18) (2019) 7268-7284.
  • [13] R. Suparatulatorn, A. Khemphet, Tseng type methods for inclusion and fixed point problems with applications, Mathematics. 7(12) (2019) 1175.
  • [14] R. Suparatulatorn, A. Khemphet, P. Charoensawan, S. Suantai, N. Phudolsitthiphat, Generalized self-adaptive algorithm for solving split common fixed point problem and its application to image restoration problem, Int. J. Comput. Math.97(7) (2020) 1431-1443.
  • [15] T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal.Appl. 340(2) (2008) 1088-1095.
  • [16] B. S. Thakur, D. Thakur, M. Postolache, A new iteration scheme for approximating fixed points of nonexpansive mappings, Filomat. 30(10) (2016) 2711-2720.
  • [17] G. I. Usurelu, A. Bejenaru, M. Postolache, Operators with property (E) as concerns numerical analysis and visualization, Numer. Funct. Anal. Optim. 41(11) (2020) 1398-1419.
  • [18] P. Cholamjiak, W. Cholamjiak, Fixed point theorems for hybrid multivalued mappings in Hilbert spaces, J. Fixed Point Theory Appl. 18 (2016) 673-688.
  • [19] P. Cholamjiak, A. A. Abdou, Y. J. Cho, Proximal point algorithms involving fixed points of nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl. 2015 (2015) 227.
  • [20] S. Kesornprom, N. Pholasa, P. Cholamjiak, On the convergence analysis of the gradient-CQ algorithms for the split feasibility problem, Numerical Algorithms. 84(3) (2020) 997-1017.
  • [21] S. Kesornprom, P. Cholamjiak, Proximal type algorithms involving linesearch and inertial technique for split variational inclusion problem in hilbert spaces with applications, Optimization. 68(12) (2019) 2369-2395.
  • [22] S. Suantai, S. Kesornprom, P. Cholamjiak, A new hybrid CQ algorithm for the split feasibility problem in Hilbert spaces and its applications to compressed sensing, Mathematics. 7(9) (2019) 789.
  • [23] R. Suparatulatorn, P. Charoensawan, K. Poochinapan, S. Dangskul, An algorithm for the split feasible problem and image restoration, RACSAM. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. 115 (2021). https://doi.org/10.1007/s13398-020-00942-z.
  • [24] R. Suparatulatorn, P. Charoensawan, A. Khemphet, An inertial subgradient extragradient method of variational inequality problems involving quasi-nonexpansive operators with applications, Math. Methods Appl. Sci. (2021).https://doi.org/10.1002/mma.7576.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Tanapat Chalarux

Khuanchanok Chaichana 0000-0003-3246-673X

Proje Numarası R000027527
Yayımlanma Tarihi 31 Aralık 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 4 Sayı: 4

Kaynak Göster

APA Chalarux, T., & Chaichana, K. (2021). Approximation of fixed points for Garcia-Falset mappings in a uniformly convex Banach space. Results in Nonlinear Analysis, 4(4), 200-206. https://doi.org/10.53006/rna.960564
AMA Chalarux T, Chaichana K. Approximation of fixed points for Garcia-Falset mappings in a uniformly convex Banach space. RNA. Aralık 2021;4(4):200-206. doi:10.53006/rna.960564
Chicago Chalarux, Tanapat, ve Khuanchanok Chaichana. “Approximation of Fixed Points for Garcia-Falset Mappings in a Uniformly Convex Banach Space”. Results in Nonlinear Analysis 4, sy. 4 (Aralık 2021): 200-206. https://doi.org/10.53006/rna.960564.
EndNote Chalarux T, Chaichana K (01 Aralık 2021) Approximation of fixed points for Garcia-Falset mappings in a uniformly convex Banach space. Results in Nonlinear Analysis 4 4 200–206.
IEEE T. Chalarux ve K. Chaichana, “Approximation of fixed points for Garcia-Falset mappings in a uniformly convex Banach space”, RNA, c. 4, sy. 4, ss. 200–206, 2021, doi: 10.53006/rna.960564.
ISNAD Chalarux, Tanapat - Chaichana, Khuanchanok. “Approximation of Fixed Points for Garcia-Falset Mappings in a Uniformly Convex Banach Space”. Results in Nonlinear Analysis 4/4 (Aralık 2021), 200-206. https://doi.org/10.53006/rna.960564.
JAMA Chalarux T, Chaichana K. Approximation of fixed points for Garcia-Falset mappings in a uniformly convex Banach space. RNA. 2021;4:200–206.
MLA Chalarux, Tanapat ve Khuanchanok Chaichana. “Approximation of Fixed Points for Garcia-Falset Mappings in a Uniformly Convex Banach Space”. Results in Nonlinear Analysis, c. 4, sy. 4, 2021, ss. 200-6, doi:10.53006/rna.960564.
Vancouver Chalarux T, Chaichana K. Approximation of fixed points for Garcia-Falset mappings in a uniformly convex Banach space. RNA. 2021;4(4):200-6.