• 제목/요약/키워드: Relatively nonexpansive mapping

검색결과 16건 처리시간 0.017초

STRONG CONVERGENCE THEOREMS FOR GENERALIZED VARIATIONAL INEQUALITIES AND RELATIVELY WEAK NONEXPANSIVE MAPPINGS IN BANACH SPACES

  • Liu, Ying
    • East Asian mathematical journal
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    • 제28권3호
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    • pp.265-280
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    • 2012
  • In this paper, we introduce an iterative sequence by using a hybrid generalized $f$-projection algorithm for finding a common element of the set of fixed points of a relatively weak nonexpansive mapping an the set of solutions of a generalized variational inequality in a Banach space. Our results extend and improve the recent ones announced by Y. Liu [Strong convergence theorems for variational inequalities and relatively weak nonexpansive mappings, J. Glob. Optim. 46 (2010), 319-329], J. Fan, X. Liu and J. Li [Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces, Nonlinear Analysis 70 (2009), 3997-4007], and many others.

THE SHRINKING PROJECTION METHODS FOR HEMI-RELATIVELY NONEXPANSIVE MAPPINGS, VARIATIONAL INEQUALITIES AND EQUILIBRIUM PROBLEMS

  • Wang, Zi-Ming;Kang, Mi Kwang;Cho, Yeol Je
    • 대한수학회논문집
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    • 제28권1호
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    • pp.191-207
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    • 2013
  • In this paper, we introduce the shrinking projection method for hemi-relatively nonexpansive mappings to find a common solution of variational inequality problems and equilibrium problems in uniformly convex and uniformly smooth Banach spaces and prove some strong convergence theorems to the common solution by using the proposed method.

APPROXIMATION METHODS FOR A COMMON MINIMUM-NORM POINT OF A SOLUTION OF VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS IN BANACH SPACES

  • Shahzad, N.;Zegeye, H.
    • 대한수학회보
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    • 제51권3호
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    • pp.773-788
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    • 2014
  • We introduce an iterative process which converges strongly to a common minimum-norm point of solutions of variational inequality problem for a monotone mapping and fixed points of a finite family of relatively nonexpansive mappings in Banach spaces. Our theorems improve most of the results that have been proved for this important class of nonlinear operators.

OUTER APPROXIMATION METHOD FOR ZEROS OF SUM OF MONOTONE OPERATORS AND FIXED POINT PROBLEMS IN BANACH SPACES

  • Abass, Hammad Anuoluwapo;Mebawondu, Akindele Adebayo;Narain, Ojen Kumar;Kim, Jong Kyu
    • Nonlinear Functional Analysis and Applications
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    • 제26권3호
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    • pp.451-474
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    • 2021
  • In this paper, we investigate a hybrid algorithm for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators which is also a common fixed point problem for finite family of relatively quasi-nonexpansive mappings and split feasibility problem in uniformly convex real Banach spaces which are also uniformly smooth. The iterative algorithm employed in this paper is design in such a way that it does not require prior knowledge of operator norm. We prove a strong convergence result for approximating the solutions of the aforementioned problems and give applications of our main result to minimization problem and convexly constrained linear inverse problem.

APPROXIMATION METHODS FOR SOLVING SPLIT EQUALITY OF VARIATIONAL INEQUALITY AND f, g-FIXED POINT PROBLEMS IN REFLEXIVE BANACH SPACES

  • Yirga Abebe Belay;Habtu Zegeye;Oganeditse A. Boikanyo
    • Nonlinear Functional Analysis and Applications
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    • 제28권1호
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    • pp.135-173
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    • 2023
  • The purpose of this paper is to introduce and study a method for solving the split equality of variational inequality and f, g-fixed point problems in reflexive real Banach spaces, where the variational inequality problems are for uniformly continuous pseudomonotone mappings and the fixed point problems are for Bregman relatively f, g-nonexpansive mappings. A strong convergence theorem is proved under some mild conditions. Finally, a numerical example is provided to demonstrate the effectiveness of the algorithm.