Ir al contenido

Documat


Convergence theorems for finding the split common null point in Banach spaces

  • Autores: Suthep Suantai, Kittipong Srisap, Natthapong Naprang, Manatsawin Mamat, Vithoon Yundon, Prasit Cholamjiak
  • Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 18, Nº. 2, 2017, págs. 345-360
  • Idioma: inglés
  • DOI: 10.4995/agt.2017.7257
  • Enlaces
  • Resumen
    • In this paper, we introduce a new iterative scheme for solving the split common null point problem. We then prove the strong convergence theorem under suitable conditions. Finally, we give some numerical examples for our results.

  • Referencias bibliográficas
    • A.S. Alofi, M. Alsulami, W. Takahashi, Strongly convergent iterative method for the split common null point problem in Banach spaces, J. Nonlinear...
    • M. Alsulami, W. Takahashi, Iterative methods for the split feasibility problem in Banach spaces, J. Convex Anal. 16 (2015), 585-596.
    • K. Aoyama, Y. Yasunori, W. Takahashi, M. Toyoda, On a strongly nonexpansive sequence in a Hilbert space, J. Nonlinear Convex Anal. 8 (2007),...
    • F. E. Browder, Nonlinear maximal monotone operators in Banach spaces, Math. Ann. 175 (1968) 89-113.
    • https://doi.org/10.1007/BF01418765
    • C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Prob. 18 (2002), 441-453.
    • https://doi.org/10.1088/0266-5611/18/2/310
    • C. Byrne, Y. Censor, A. Gibili, S. Reich, The split common null point problem. J. Nonlinear Convex Anal. 13 (2012), 759-775.
    • B. Halpern, Fixed point of nonexpanding maps, Bull. Amer. Math. Soc. 73(1967), 506-961.
    • https://doi.org/10.1090/S0002-9904-1967-11864-0
    • Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections in product space, Numer. Algorithms. 8 (1994), 221-239
    • https://doi.org/10.1007/BF02142692
    • P.E. Mainge, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Anal. 16 (2008),...
    • https://doi.org/10.1007/s11228-008-0102-z
    • W. R. Mann, Mean value methods in it iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510.
    • https://doi.org/10.1090/S0002-9939-1953-0054846-3
    • A. Moudafi, Split monotone variational inclusions, J. Optim. Theory Appl. 150 (2011), 275-283.
    • https://doi.org/10.1007/s10957-011-9814-6
    • A. Moudafi, Viscosity approximation method for fixed-points problems, J. Math. Anal. Appl. 241 (2000), 46-55.
    • https://doi.org/10.1006/jmaa.1999.6615
    • A. Moudafi, B. S. Thakur, Solving proximal split feasibility problems without prior knowledge of operator norms, Optim. Lett. 8 (2014), 2099-2110.
    • https://doi.org/10.1007/s11590-013-0708-4
    • W. Takahashi, Convex Analysis and Approximation of Fixed Point, Yokohama Publishers,Yokohama, 2009.
    • W. Takahashi, Introduction to Nonlinear and Convex Analysis, Yokohama Publishers, Yokohama, 2009.
    • W. Takahashi, Nonlinear Functional Analysis, Yokohama, Publishers, Yokohama, 2000.
    • F. Wang, A new algorithm for solving the multiple-sets split feasibility problem in certain Banach spaces, Numer. Funct. Anal. Optim. 35 (2014),...
    • https://doi.org/10.1080/01630563.2013.809360
    • H. K. Xu, Another control condition in an iterative method for nonexpansive mappings, Bull. Austral. Math. Soc. 65 (2002), 109-113.
    • https://doi.org/10.1017/S0004972700020116

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno