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Weak and Strong Convergence of Hybrid Subgradient Method for Pseudomonotone Equilibrium Problems and Nonspreading- Type Mappings in Hilbert Spaces

Wanna Sriprad|Somnuk Srisawat
경북대학교 자연과학대학 수학과|2019.03|Kyungpook Mathematical Journal|제59권 제1호|pp. 83-99|DOI 10.5666/KMJ.2019.59.1.83

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참고문헌

키워드

fixed pointnonspreading mappingpseudomonotone equilibrium problemk -strictly presudonon-spreading mappinghybrid subgradient method
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초록

In this paper, we introduce a hybrid subgradient method for finding an element common to both the solution set of a class of pseudomonotone equilibrium problems, and the set of fixed points of a finite family of k-strictly presudononspreading mappings in a real Hilbert space. We establish some weak and strong convergence theorems of the sequences generated by our iterative method under some suitable conditions. These convergence theorems are investigated without the Lipschitz condition for bifunctions. Our results complement many known recent results in the literature.

Abstract

In this paper, we introduce a hybrid subgradient method for finding an element common to both the solution set of a class of pseudomonotone equilibrium problems, and the set of fixed points of a finite family of k-strictly presudononspreading mappings in a real Hilbert space. We establish some weak and strong convergence theorems of the sequences generated by our iterative method under some suitable conditions. These convergence theorems are investigated without the Lipschitz condition for bifunctions. Our results complement many known recent results in the literature.

참고문헌 (23)

  1. P. N. Anh, "Strong convergence theorems for nonexpansive mappings and Ky Fan inequalities", J. Optim. Theory Appl, 154, pp.303~320 (2012)
  2. P. N. Anh, "A hybrid extragradient method extended to fixed point problems and equilibrium problems", Optimization, 62(2), pp.271~283 (2013)
  3. P. N. Anh, "A hybrid subgradient algorithm for nonexpansive mappings and equilibrium problems", Optim. Lett, 8, pp.727~738 (2014)
  4. P.N. Anh, "A NEW METHOD FOR A FINITE FAMILY OF PSEUDOCONTRACTIONS AND EQUILIBRIUM PROBLEMS", Journal of Applied Mathematics and Informatics, 29(5), pp.1179~1191 (2011), 한국전산응용수학회
  5. K. Aoyama, "Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space", Nonlinear Anal, 67, pp.2350~2360 (2007)
  6. A. Auslender, "A logarithmic quadratic proximal method for variational inequalities", Comput. Optim. Appl, 12, pp.31~40 (1999)
  7. J. Baillon, "Un theoreme de type ergodique pour les contractions nonlineaires dans un espace de Hilbert", C. R. Acad. Sci. Paris Ser. A-B, 280, pp.A1511~A1514 (1975)[DOI]
  8. E. Blum, "From optimization and variational inequalities to equilibrium problems", Math. Student, 63, pp.123~145 (1994)
  9. A. Brndsted, "On the subdifferentiability of convex functions", Proc. Am. Math. Soc, 16, pp.605~611 (1965)
  10. F. E. Browder, "Construction of fixed points of nonlinear mappings in Hilbert space", J. Math. Anal. Appl, 20, pp.197~228 (1967)
  11. P. L. Combettes, "Equilibrium programming in Hilbert spaces", J. Nonlinear Convex Anal, 6, pp.117~136 (2005)
  12. B. Halpern, "Fixed points of nonexpanding maps", Bull. Amer. Math. Soc, 73, pp.957~961 (1967)
  13. J.-B. Hiriart-Urruty, "ε-Subdifferential calculus, Convex Analysis and Optimization", Res. Notes in Math, 57, pp.43~92 (1982)
  14. A. Kangtunyakarn, "The methods for variational inequality problems and fixed point of κ-strictly pseudononspreading mapping", Fixed Point Theory Appl., 171(2013), pp.15~ (2013)
  15. F. Kohsaka, "Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces", Arch. Math. (Basel), 91, pp.166~177 (2008)
  16. Y. Kurokawa, "Weak and strong convergence theorems for nonspreading mappings in Hilbert spaces", Nonlinear Anal, 73(6), pp.1562~1568 (2010)
  17. M. O. Osilike, "Weak and strong convergence theorems for nonspreading-type mappings in Hilbert spaces", Nonlinear Anal, 74(5), pp.1814~1822 (2011)
  18. P. Santos, "An inexact subgradient algorithm for equilibrium problems", Comput. Appl. Math, 30, pp.91~107 (2011)
  19. W. Takahashi, "Introduction to nonlinear and Convex Analysis" (2009), Yokohama Publishers
  20. S. Takahashi, "Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces", J. Math. Anal. Appl, 331(1), pp.506~515 (2007)
  21. E. Thailert, "A Hybrid subgradient algorithm for finding a common solution of an equilibrium problem and a family of strict pseudocontraction mappings", J. Appl. Math, pp.8~ (2014)[DOI]
  22. E. Thailert, "A new general iterative methods for solving the equilibrium problems, variational inequality problems and fixed point problems of nonexpansive mappings", Thai J. Math, 14(1), pp.53~67 (2016)
  23. H. -K. Xu, "Viscosity approximation methods for nonexpansive mappings", J. Math. Anal. Appl, 298, pp.279~291 (2004)

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WEAK CONVERGENCE THEOREMS FOR GENERALIZED MIXED EQUILIBRIUM PROBLEMS, MONOTONE MAPPINGS AND PSEUDOCONTRACTIVE MAPPINGS정종수대한수학회 · 대한수학회지2015 · 제52권 제6호A HYBRID ITERATIVE METHOD OF SOLUTION FOR MIXED EQUILIBRIUM AND OPTIMIZATION PROBLEMSJunmin Chen, Lijuan Zhang영남수학회 · East Asian Mathematical Journal2010 · 제26권 제1호Weak and strong convergence theorems for a system of mixed equilibrium problems and a nonexpansive mapping in Hilbert spacesKamonrat Sombut, Somyot Plubtieng대한수학회 · 대한수학회보2013 · 제50권 제2호Fixed point solution methods for solving equilibrium problemsNguyen Duc Hien, Pham Ngoc Anh대한수학회 · 대한수학회보2014 · 제51권 제2호A PARALLEL HYBRID METHOD FOR EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITIES AND NONEXPANSIVE MAPPINGS IN HILBERT SPACEDang Van Hieu대한수학회 · 대한수학회지2015 · 제52권 제2호A hybrid projection method for relaxed cocoercive mappings and strictly pseudo-contractive mappingsYing Liu영남수학회 · East Asian Mathematical Journal2012 · 제28권 제3호

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