• Title/Summary/Keyword: uniformly Lipschitzian mapping

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STRONG CONVERGENCE THEOREM FOR UNIFORMLY L-LIPSCHITZIAN MAPPINGS IN BANACH SPACES

  • Qin, Xiaolong;Kang, Shin Min;Shang, Meijuan
    • Journal of the Chungcheong Mathematical Society
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    • v.21 no.3
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    • pp.293-299
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    • 2008
  • In this paper, we prove strong convergence theorems for a finite family of uniformly L-Lipschitzian mappings by a cyclic iterative algorithm in the framework of Banach spaces. Our results improve and extend the recent ones announced by many others.

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THE CONVERGENCE THEOREMS FOR COMMON FIXED POINTS OF UNIFORMLY L-LIPSCHITZIAN ASYMPTOTICALLY Φ-PSEUDOCONTRACTIVE MAPPINGS

  • Xue, Zhiqun
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.2
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    • pp.295-305
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    • 2010
  • In this paper, we show that the modified Mann iteration with errors converges strongly to fixed point for uniformly L-Lipschitzian asymptotically $\Phi$-pseudocontractive mappings in real Banach spaces. Meanwhile, it is proved that the convergence of Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitzian asymptotically $\Phi$-pseudocontractive mappings in real Banach spaces. Finally, we obtain the convergence theorems of Ishikawa iterative sequence and the modified Ishikawa iterative process with errors.

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.

A HYBRID METHOD FOR A COUNTABLE FAMILY OF LIPSCHITZ GENERALIZED ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS AND AN EQUILIBRIUM PROBLEM

  • Cholamjiak, Prasit;Cholamjiak, Watcharaporn;Suantai, Suthep
    • Communications of the Korean Mathematical Society
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    • v.28 no.2
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    • pp.335-351
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    • 2013
  • In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings and the solutions set of equilibrium problems. Some strong convergence theorems of the proposed iterative scheme are established by using the concept of W-mappings of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings.

CONVERGENCE OF APPROXIMATING PATHS TO SOLUTIONS OF VARIATIONAL INEQUALITIES INVOLVING NON-LIPSCHITZIAN MAPPINGS

  • Jung, Jong-Soo;Sahu, Daya Ram
    • Journal of the Korean Mathematical Society
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    • v.45 no.2
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    • pp.377-392
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    • 2008
  • Let X be a real reflexive Banach space with a uniformly $G\hat{a}teaux$ differentiable norm, C a nonempty closed convex subset of X, T : C $\rightarrow$ X a continuous pseudocontractive mapping, and A : C $\rightarrow$ C a continuous strongly pseudocontractive mapping. We show the existence of a path ${x_t}$ satisfying $x_t=tAx_t+(1- t)Tx_t$, t $\in$ (0,1) and prove that ${x_t}$ converges strongly to a fixed point of T, which solves the variational inequality involving the mapping A. As an application, we give strong convergence of the path ${x_t}$ defined by $x_t=tAx_t+(1-t)(2I-T)x_t$ to a fixed point of firmly pseudocontractive mapping T.

ON ASYMPTOTICALLY DEMICONTRACTIVE MAPPINGS IN ARBITRARY BANACH SPACES

  • Rafiq, Arif;Lee, Byung Soo
    • East Asian mathematical journal
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    • v.28 no.5
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    • pp.569-578
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    • 2012
  • In this paper, the necessary and sufficient conditions for the strong convergence of a modified Mann iteration process to a fixed point of an asymptotically demicontractive mapping in real Banach spaces are considered. Presented results improve and extend the results of Igbokwe [3], Liu [4], Moore and Nnoli [6] and Osilike [7].

Noor Iterations with Error for Non-Lipschitzian Mappings in Banach Spaces

  • Plubtieng, Somyot;Wangkeeree, Rabian
    • Kyungpook Mathematical Journal
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    • v.46 no.2
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    • pp.201-209
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    • 2006
  • Suppose C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T : $C{\rightarrow}C$ be an asymptotically nonexpansive in the intermediate sense mapping. In this paper we introduced the three-step iterative sequence for such map with error members. Moreover, we prove that, if T is completely continuous then the our iterative sequence converges strongly to a fixed point of T.

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A NEW APPROXIMATION SCHEME FOR FIXED POINTSOF ASYMPTOTICALLY ø-HEMICONTRACTIVE MAPPINGS

  • Kim, Seung-Hyun;Lee, Byung-Soo
    • Communications of the Korean Mathematical Society
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    • v.27 no.1
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    • pp.167-174
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    • 2012
  • In this paper, we introduce an asymptotically $\phi$-hemicontractive mapping with a $\phi$-normalized duality mapping and obtain some strongly convergent result of a kind of multi-step iteration schemes for asymptotically $\phi$-hemicontractive mappings.