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Algorithm analysis of solving fixed point of nonexpansive mappings based on runge-kutta method

Yıl 2023, Cilt: 52 Sayı: 6 - Special Issue: Nonlinear Evolution Problems with Applications, 1567 - 1577, 03.11.2023

Öz

In order to solve the fixed point of nonexpansive mappings, we propose two iterative algorithms based on runge-kutta method. The first algorithm is focused on solving the fixed point problem of a single nonexpansive mapping, and weak convergence has been proved. we suggest the second algorithm by dynamic string-averaging rule. It can be used to find a common fixed point of a family of finite nonexpansive mappings. We show that the second algorithm is bounded perturbations resilient, and it is strongly convergent.

Destekleyen Kurum

National Natural Science Foundation of China

Proje Numarası

11861003

Kaynakça

  • [1] M. A. Alghamdi, M. A. Alghamdi, N. Shahzad and H. K. Xu, The implicit midpoint rule for nonexpansive mappings, Fixed Point Theory and Applications, 96, 1-9, 2014.
  • [2] L. C. Ceng, D. R. Sahu and J. C. Yao, Implicit iterative algorithms for asymptotically nonexpansive mappings in the intermediate sense and Lipschitz-continuous monotone mappings, J. Comput. Appl. 11, 2902-2915, 2010.
  • [3] L. C. Ceng, N. C. Wong and J. C. Yao, Strong and weak convergence theorems for an infinite family of nonexpansive mappings and applications, Fixed Point Theory and Applications, 117, 2012.
  • [4] Y. Censor, R. Davidi and G. T. Herman, Perturbation resilience and superiorization of iterative algorithms, Inverse Probl. 26, 065008, 2010.
  • [5] Y. Censor and A. J. Zaslavski, Convergence and perturbation resilience of dynamic string-averaging projection methods, Comput. Optim. Appl. 54, 65-76, 2013.
  • [6] P. Deuflhard, Recent progress in extrapolation methods for ordinary differential equations, SIAM Rev. 27, 505-535, 1985.
  • [7] B. Halpern, Fixed points of nonexpanding maps, Bull. Amer. Math. Soc. 73, 957-961, 1967.
  • [8] L. He, L. J. Zhu and Y. M. Fu, An iterative algorithm based on simpson methods for solving fixed point problem of nonexpansive mappings, UPB Sci. Bull. A: Appl. Math. Phys. 83, 13-20, 2021.
  • [9] S. Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces , J. Math. Anal. Appl. 67, 274-276, 1979.
  • [10] H. K. Xun and R. G. Ori, An implicit iteration process for nonexpansive mappings , Numer. Funct. Anal. Optim. 22, 767-773, 2001.
  • [11] Y. H. Yao, Y. C. Liou, T. L. Lee and N. C. Wong, An iterative algorithm based on the implicit midpoint rule for nonexpansive mappings, J. Nonlinear Convex Anal. 17, 655-668, 2016.
  • [12] A. J. Zaslavski Approximate solutions of common fixed point problems, Commun. Appl. Nonlinear Anal. 22, 80-89, 2015.
  • [13] A. J. Zaslavski, Asymptotic behavior of two algorithms for solving common fixed point problems, Inverse Probl. 33, 044004, 2017.
  • [14] A. J. Zaslavski, Algorithms for Solving Common Fixed Point Problems, Springer Science and Business Media LLC. 2018.
  • [15] H. Y. Zhou, X. L. Qin, Fixed Points of Nonlinear Operators, Walter de Gruyter GmbH. 2020.
  • [16] L. J. Zhu, M. Postolache and Y. Y. She, Convergence of self-adaptive projection methods with linear search for pseudomonotone variational inequalities and fixed point problems , J. Nonlinear Convex Anal. 22, 1541-1554, 2021.
  • [17] L. J. Zhu, Y. H. Yao and M. Postolache, Projection methods with linesearch technique for pseudomonotone equilibrium problems and fixed point problems, UPB Sci. Bull. A: Appl. Math. Phys. 83, 3-14, 2021.
Yıl 2023, Cilt: 52 Sayı: 6 - Special Issue: Nonlinear Evolution Problems with Applications, 1567 - 1577, 03.11.2023

Öz

Proje Numarası

11861003

Kaynakça

  • [1] M. A. Alghamdi, M. A. Alghamdi, N. Shahzad and H. K. Xu, The implicit midpoint rule for nonexpansive mappings, Fixed Point Theory and Applications, 96, 1-9, 2014.
  • [2] L. C. Ceng, D. R. Sahu and J. C. Yao, Implicit iterative algorithms for asymptotically nonexpansive mappings in the intermediate sense and Lipschitz-continuous monotone mappings, J. Comput. Appl. 11, 2902-2915, 2010.
  • [3] L. C. Ceng, N. C. Wong and J. C. Yao, Strong and weak convergence theorems for an infinite family of nonexpansive mappings and applications, Fixed Point Theory and Applications, 117, 2012.
  • [4] Y. Censor, R. Davidi and G. T. Herman, Perturbation resilience and superiorization of iterative algorithms, Inverse Probl. 26, 065008, 2010.
  • [5] Y. Censor and A. J. Zaslavski, Convergence and perturbation resilience of dynamic string-averaging projection methods, Comput. Optim. Appl. 54, 65-76, 2013.
  • [6] P. Deuflhard, Recent progress in extrapolation methods for ordinary differential equations, SIAM Rev. 27, 505-535, 1985.
  • [7] B. Halpern, Fixed points of nonexpanding maps, Bull. Amer. Math. Soc. 73, 957-961, 1967.
  • [8] L. He, L. J. Zhu and Y. M. Fu, An iterative algorithm based on simpson methods for solving fixed point problem of nonexpansive mappings, UPB Sci. Bull. A: Appl. Math. Phys. 83, 13-20, 2021.
  • [9] S. Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces , J. Math. Anal. Appl. 67, 274-276, 1979.
  • [10] H. K. Xun and R. G. Ori, An implicit iteration process for nonexpansive mappings , Numer. Funct. Anal. Optim. 22, 767-773, 2001.
  • [11] Y. H. Yao, Y. C. Liou, T. L. Lee and N. C. Wong, An iterative algorithm based on the implicit midpoint rule for nonexpansive mappings, J. Nonlinear Convex Anal. 17, 655-668, 2016.
  • [12] A. J. Zaslavski Approximate solutions of common fixed point problems, Commun. Appl. Nonlinear Anal. 22, 80-89, 2015.
  • [13] A. J. Zaslavski, Asymptotic behavior of two algorithms for solving common fixed point problems, Inverse Probl. 33, 044004, 2017.
  • [14] A. J. Zaslavski, Algorithms for Solving Common Fixed Point Problems, Springer Science and Business Media LLC. 2018.
  • [15] H. Y. Zhou, X. L. Qin, Fixed Points of Nonlinear Operators, Walter de Gruyter GmbH. 2020.
  • [16] L. J. Zhu, M. Postolache and Y. Y. She, Convergence of self-adaptive projection methods with linear search for pseudomonotone variational inequalities and fixed point problems , J. Nonlinear Convex Anal. 22, 1541-1554, 2021.
  • [17] L. J. Zhu, Y. H. Yao and M. Postolache, Projection methods with linesearch technique for pseudomonotone equilibrium problems and fixed point problems, UPB Sci. Bull. A: Appl. Math. Phys. 83, 3-14, 2021.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Xiangyao Li 0000-0002-0877-7995

Li-jun Zhu 0000-0001-8883-5034

Mihai Postolache 0000-0003-0738-787X

Proje Numarası 11861003
Yayımlanma Tarihi 3 Kasım 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 52 Sayı: 6 - Special Issue: Nonlinear Evolution Problems with Applications

Kaynak Göster

APA Li, X., Zhu, L.-j., & Postolache, M. (2023). Algorithm analysis of solving fixed point of nonexpansive mappings based on runge-kutta method. Hacettepe Journal of Mathematics and Statistics, 52(6), 1567-1577.
AMA Li X, Zhu Lj, Postolache M. Algorithm analysis of solving fixed point of nonexpansive mappings based on runge-kutta method. Hacettepe Journal of Mathematics and Statistics. Kasım 2023;52(6):1567-1577.
Chicago Li, Xiangyao, Li-jun Zhu, ve Mihai Postolache. “Algorithm Analysis of Solving Fixed Point of Nonexpansive Mappings Based on Runge-Kutta Method”. Hacettepe Journal of Mathematics and Statistics 52, sy. 6 (Kasım 2023): 1567-77.
EndNote Li X, Zhu L-j, Postolache M (01 Kasım 2023) Algorithm analysis of solving fixed point of nonexpansive mappings based on runge-kutta method. Hacettepe Journal of Mathematics and Statistics 52 6 1567–1577.
IEEE X. Li, L.-j. Zhu, ve M. Postolache, “Algorithm analysis of solving fixed point of nonexpansive mappings based on runge-kutta method”, Hacettepe Journal of Mathematics and Statistics, c. 52, sy. 6, ss. 1567–1577, 2023.
ISNAD Li, Xiangyao vd. “Algorithm Analysis of Solving Fixed Point of Nonexpansive Mappings Based on Runge-Kutta Method”. Hacettepe Journal of Mathematics and Statistics 52/6 (Kasım 2023), 1567-1577.
JAMA Li X, Zhu L-j, Postolache M. Algorithm analysis of solving fixed point of nonexpansive mappings based on runge-kutta method. Hacettepe Journal of Mathematics and Statistics. 2023;52:1567–1577.
MLA Li, Xiangyao vd. “Algorithm Analysis of Solving Fixed Point of Nonexpansive Mappings Based on Runge-Kutta Method”. Hacettepe Journal of Mathematics and Statistics, c. 52, sy. 6, 2023, ss. 1567-7.
Vancouver Li X, Zhu L-j, Postolache M. Algorithm analysis of solving fixed point of nonexpansive mappings based on runge-kutta method. Hacettepe Journal of Mathematics and Statistics. 2023;52(6):1567-7.