• 제목/요약/키워드: non-expansive mapping

검색결과 13건 처리시간 0.021초

U-FLATNESS AND NON-EXPANSIVE MAPPINGS IN BANACH SPACES

  • Gao, Ji;Saejung, Satit
    • 대한수학회지
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    • 제54권2호
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    • pp.493-506
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    • 2017
  • In this paper, we define the modulus of n-dimensional U-flatness as the determinant of an $(n+1){\times}(n+1)$ matrix. The properties of the modulus are investigated and the relationships between this modulus and other geometric parameters of Banach spaces are studied. Some results on fixed point theory for non-expansive mappings and normal structure in Banach spaces are obtained.

Approximation of Common Fixed Points of Mean Non-expansive Mapping in Banach Spaces

  • Gu, Zhaohui;Li, Yongjin
    • Kyungpook Mathematical Journal
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    • 제54권1호
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    • pp.103-111
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    • 2014
  • Let X be a uniformly convex Banach space, and S, T be pair of mean nonexpansive mappings. Some necessary and sufficient conditions are given for Ishikawa iterative sequence converge to common fixed points, and we prove that the sequence of Ishikawa iterations associated with S and T converges to the common fixed point of S and T. This generalizes former results proved by Z. Gu and Y. Li [4].

COMMON FIXED POINT THEOREMS FOR TWO MAPPINGS WITH ψ-ϕ-CONTRACTIVE OR EXPANSIVE TYPE CONDITIONS ON COMPLEX-VALUED METRIC SPACES

  • JIN, HAI-LAN;PIAO, YONG-JIE
    • 충청수학회지
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    • 제28권3호
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    • pp.451-463
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    • 2015
  • A continuous and non-decreasing function ${\psi}$ and another continuous function ${\phi}$ with ${\phi}(z)=0{\Leftrightarrow}z=0$ defined on $\mathbb{C}^+=\{x+yi:x,y{\geq}0\}$ are introduced, the ${\psi}-{\phi}$-contractive or expansive type conditions are considered, and the existence theorems of common fixed points for two mappings defined on a complex valued metric space are obtained. Also, Banach contraction principle and a fixed point theorem for a I-expansive type mapping are given on complex valued metric spaces.

NON-CONVEX HYBRID ALGORITHMS FOR A FAMILY OF COUNTABLE QUASI-LIPSCHITZ MAPPINGS CORRESPONDING TO KHAN ITERATIVE PROCESS AND APPLICATIONS

  • NAZEER, WAQAS;MUNIR, MOBEEN;NIZAMI, ABDUL RAUF;KAUSAR, SAMINA;KANG, SHIN MIN
    • Journal of applied mathematics & informatics
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    • 제35권3_4호
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    • pp.313-321
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    • 2017
  • In this note we establish a new non-convex hybrid iteration algorithm corresponding to Khan iterative process [4] and prove strong convergence theorems of common fixed points for a uniformly closed asymptotically family of countable quasi-Lipschitz mappings in Hilbert spaces. Moreover, the main results are applied to get the common fixed points of finite family of quasi-asymptotically nonexpansive mappings. The results presented in this article are interesting extensions of some current results.

NEW HYBRID ALGORITHM FOR WEAK RELATIVELY NONEXPANSIVE MAPPING AND INVERSE-STRONGLY MONOTONE MAPPING IN BANACH SPACE

  • Zhang, Xin;Su, Yongfu;Kang, Jinlong
    • Journal of applied mathematics & informatics
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    • 제29권1_2호
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    • pp.87-102
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    • 2011
  • The purpose of this paper is to prove strong convergence theorems for finding a common element of the set of fixed points of a weak relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping by a new hybrid method in a Banach space. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping in Banach space $l^2$. Our results improve and extend the corresponding results announced by Ying Liu[Ying Liu, Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space, Appl. Math. Mech. -Engl. Ed. 30(7)(2009), 925-932] and some others.

STRONG CONVERGENCE OF MODIFIED ISHIKAWA ITERATES FOR ASYMPTOTICALLY NONEXPANSIVE MAPS WITH NEW CONTROL CONDITIONS

  • Eldred, A. Anthony;Mary, P. Julia
    • 대한수학회논문집
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    • 제33권4호
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    • pp.1271-1284
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    • 2018
  • In this paper, we establish strong convergence of the modified Ishikawa iterates of an asymptotically non expansive self-mapping of a nonempty closed bounded and convex subset of a uniformly convex Banach space under a variety of new control conditions.

STRONG CONVERGENCE OF A NEW ITERATIVE ALGORITHM FOR AVERAGED MAPPINGS IN HILBERT SPACES

  • Yao, Yonghong;Zhou, Haiyun;Chen, Rudong
    • Journal of applied mathematics & informatics
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    • 제28권3_4호
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    • pp.939-944
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    • 2010
  • Let H be a real Hilbert space. Let T : $H\;{\rightarrow}\;H$ be an averaged mapping with $F(T)\;{\neq}\;{\emptyset}$. Let {$\alpha_n$} be a real numbers in (0, 1). For given $x_0\;{\in}\;H$, let the sequence {$x_n$} be generated iteratively by $x_{n+1}\;=\;(1\;-\;{\alpha}_n)Tx_n$, $n\;{\geq}\;0$. Assume that the following control conditions hold: (i) $lim_{n{\rightarrow}{\infty}}\;{\alpha}_n\;=\;0$; (ii) $\sum^{\infty}_{n=0}\;{\alpha}_n\;=\;{\infty}$. Then {$x_n$} converges strongly to a fixed point of T.

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.

Algorithm of Common Solutions to the Cayley Inclusion and Fixed Point Problems

  • Dar, Aadil Hussain;Ahmad, Mohammad Kalimuddin;Iqbal, Javid;Mir, Waseem Ali
    • Kyungpook Mathematical Journal
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    • 제61권2호
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    • pp.257-267
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    • 2021
  • In this paper, we develop an iterative algorithm for obtaining common solutions to the Cayley inclusion problem and the set of fixed points of a non-expansive mapping in Hilbert spaces. A numerical example is given for the justification of our claim.