• Title, Summary, Keyword: convex metric space

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THE PROXIMAL POINT ALGORITHM IN UNIFORMLY CONVEX METRIC SPACES

  • Choi, Byoung Jin;Ji, Un Cig
    • Communications of the Korean Mathematical Society
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    • v.31 no.4
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    • pp.845-855
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    • 2016
  • We introduce the proximal point algorithm in a p-uniformly convex metric space. We first introduce the notion of p-resolvent map in a p-uniformly convex metric space as a generalization of the Moreau-Yosida resolvent in a CAT(0)-space, and then we secondly prove the convergence of the proximal point algorithm by the p-resolvent map in a p-uniformly convex metric space.

FIXED POINTS OF BETTER ADMISSIBLE MAPS ON GENERALIZED CONVEX SPACES

  • Park, Se-Hie
    • Journal of the Korean Mathematical Society
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    • v.37 no.6
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    • pp.885-899
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    • 2000
  • We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.

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CONVERGENCE OF A NEW MULTISTEP ITERATION IN CONVEX CONE METRIC SPACES

  • Gunduz, Birol
    • Communications of the Korean Mathematical Society
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    • v.32 no.1
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    • pp.39-46
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    • 2017
  • In this paper, we propose a new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex cone metric spaces. Then we show that our iteration converges to a common fixed point of this class of mappings under suitable conditions. Our result generalizes the corresponding result of Lee [5] from the closed convex subset of a convex cone metric space to whole space.

On compact convex subsets of fuzzy number space (퍼지 수 공간의 컴팩트 볼륵 집합에 관한 연구)

  • Kim, Yun-Kyong
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.14-17
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    • 2003
  • By Mazur's theorem, the convex hull of a relatively compact subset a Banach space is also relatively compact. But this is not true any more in the space of fuzzy numbers endowed with the Hausdorff-Skorohod metric. In this paper, we establish a necessary and sufficient condition for which the convex hull of K is also relatively compact when K is a relatively compact subset of the space F(R$\^$k/) of fuzzy numbers of R$\^$k/ endowed with the Hausdorff-Skorohod metric.

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COMMON FIXED POINTS OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS BY ONE-STEP ITERATION PROCESS IN CONVEX METRIC SPACES

  • Abbas, Mujahid;Khan, Safeer Hussain;Kim, Jong-Kyu
    • East Asian mathematical journal
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    • v.26 no.5
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    • pp.693-702
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    • 2010
  • We study one-step iteration process to approximate common fixed points of two nonexpansive mappings and prove some convergence theorems in convex metric spaces. Using the so-called condition (A'), the convergence of iteratively defined sequences in a uniformly convex metric space is also obtained.

Some Notes on Lp-metric Space of Fuzzy Sets

  • Kim, Yun-Kyong
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.10 no.3
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    • pp.242-246
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    • 2010
  • It is well-known that the space $E^n$ of fuzzy numbers(i.e., normal, upper-semicontinuous, compact-supported and convex fuzzy subsets)in the n-dimensional Euclidean space $R^n$ is separable but not complete with respect to the $L_p$-metric. In this paper, we introduce the space $F_p(R^n)$ that is separable and complete with respect to the $L_p$-metric. This will be accomplished by assuming p-th mean bounded condition instead of compact-supported condition and by removing convex condition.

COMMON FIXED POINT AND INVARIANT APPROXIMATION IN MENGER CONVEX METRIC SPACES

  • Hussain, Nawab;Abbas, Mujahid;Kim, Jong-Kyu
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.4
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    • pp.671-680
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    • 2008
  • Necessary conditions for the existence of common fixed points for noncommuting mappings satisfying generalized contractive conditions in a Menger convex metric space are obtained. As an application, related results on best approximation are derived. Our results generalize various well known results.

COMMON FIXED POINTS AND INVARIANT APPROXIMATIONS FOR SUBCOMPATIBLE MAPPINGS IN CONVEX METRIC SPACE

  • Nashine, Hemant Kumar;Kim, Jong-Kyu
    • East Asian mathematical journal
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    • v.26 no.1
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    • pp.39-47
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    • 2010
  • Existence of common fixed points for generalized S-nonexpansive subcompatible mappings in convex metric spaces have been obtained. Invariant approximation results have also been derived by its application. These results extend and generalize various known results in the literature with the aid of more general class of noncommuting mappings.

STRONG CONVERGENCE IN NOOR-TYPE ITERATIVE SCHEMES IN CONVEX CONE METRIC SPACES

  • LEE, BYUNG-SOO
    • The Pure and Applied Mathematics
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    • v.22 no.2
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    • pp.185-197
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    • 2015
  • The author considers a Noor-type iterative scheme to approximate com- mon fixed points of an infinite family of uniformly quasi-sup(fn)-Lipschitzian map- pings and an infinite family of gn-expansive mappings in convex cone metric spaces. His results generalize, improve and unify some corresponding results in convex met- ric spaces [1, 3, 9, 16, 18, 19] and convex cone metric spaces [8].

S-ITERATION PROCESS FOR ASYMPTOTIC POINTWISE NONEXPANSIVE MAPPINGS IN COMPLETE HYPERBOLIC METRIC SPACES

  • Atsathi, Thikamporn;Cholamjiak, Prasit;Kesornprom, Suparat;Prasong, Autchara
    • Communications of the Korean Mathematical Society
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    • v.31 no.3
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    • pp.575-583
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    • 2016
  • In this paper, we study the modified S-iteration process for asymptotic pointwise nonexpansive mappings in a uniformly convex hyperbolic metric space. We then prove the convergence of the sequence generated by the modified S-iteration process.