본문 바로가기
KERD
논문KCI 등재

Weak convergence of an iterative method for equilibrium problems and relatively nonexpansive mappings

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

The purpose of this paper is to consider an iterative method for an equilibrium problem and a family relatively nonexpansive mappings. Weak convergence theorems are established in uniformly smooth and uniformly convex Banach spaces.

Abstract

The purpose of this paper is to consider an iterative method for an equilibrium problem and a family relatively nonexpansive mappings. Weak convergence theorems are established in uniformly smooth and uniformly convex Banach spaces.

참고문헌 (23)

  1. Ya. I. Alber, "An iterative method for solving a class of nonlinear operator equations in Banach spaces", Panamer. Math. J., 7, pp.39~54 (1994)
  2. Ya. I. Alber, "Metric and generalized projection operators in Banach spaces: properties and applications. in: Theory and Applications of Nonlinear Operators of Accretive and Monotone Type" (1996), Marcel Dekker
  3. D. Butnariu, "Asymptotic behavior of relatively nonexpansive operators in Banach spaces", J. Appl. Anal., 7, pp.151~174 (2001)
  4. D. Butnariu, "Weak convergence of orbits of nonlin-ear operators in reflexive Banach spaces", Numer. Funct. Anal. Optim., 24, pp.489~508 (2003)
  5. E. Blum, "From optimization and variational inequalities to equi-librium problems", Math. Student, 63, pp.123~145 (1994)
  6. I. Cioranescu, "Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems" (1990), Kluwer
  7. Y. J. Cho, "Approximation of common fixed points of an in¯nite family of nonexpansive mappings in Banach spaces", Comput. Math. Appl., 56, pp.2058~2064 (2008)
  8. V. Colao, "An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings", Nonlinear Anal., 71, pp.2708~2715 (2009)
  9. P. L. Combettes, "Equilibrium programming in Hilbert spaces", J. Nonlinear Convex Anal., 6, pp.117~136 (2005)
  10. O. Chadli, "Equilibrium problems with applications to eigenvalue problems", J. Optim. Theory Appl., 117, pp.245~266 (2003)
  11. S. S. Chang, "A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization", Nonlinear Anal., 70, pp.3307~3319 (2009)
  12. S. Kamimura, "Strong convergence of a proximal-type algo-rithm in a Banach space", SIAM J. Optim., 13, pp.938~945 (2002)
  13. S. Y. Matsushita, "Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces", Fixed Point Theory Appl., 2004, pp.37~47 (2004)
  14. S. Y. Matsushita, "A strong convergence theorem for relatively nonexpansive mappings in a Banach space", J. Approx. Theory, 134, pp.257~266 (2005)
  15. A. Moudafi, "Weak convergence theorems nonexpansive mappings and for equi-librium problems", J. Nonlinear Convex Anal., 9, pp.37~43 (2008)
  16. X. Qin, "Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces", J. Comput. Appl. Math., 225, pp.20~30 (2009)
  17. X. Qin, "Strong convergence of a general iterative algorithm for equilibrium problems and variational inequality problems", Math. Comput. Modelling., 48, pp.1033~1046 (2008)
  18. X. Qin, "Strong convergence theorems for an infinite family of nonexpansive mappings in Banach spaces", J. Comput. Appl. Math., 230, pp.121~127 (2009)
  19. S. Reich, "A weak convergence theorem for the alternating method with Breg-man distance. in: Theory and Applicationsof Nonlinear Operators of Accretive and Monotone Type" (1996), Marcel Dekker
  20. W. Takahashi, "Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces", Nonlinear Anal., 70, pp.45~57 (2009)
  21. W. Takahashi, "Nonlinear Functional Analysis" (2000), Yokohama-Publishers
  22. H. K. Xu, "Inequalities in Banach spaces with applications", Nonlinear Anal., 16, pp.1127~1138 (1991)
  23. D. C. Youla, "Mathematical theory of image restoration by the method of con-vex projections. in: Image Recovery: Theory and Applications", pp.29~77 (1987), Academic Press

관련 논문AI추천

이 간행물의 다른 논문 (10건)