• 제목/요약/키워드: Mann sequence

검색결과 42건 처리시간 0.027초

A NECESSARY AND SUFFICIENT CONDITION FOR THE CONVERGENCE OF THE MANN SEQUENCE FOR A CLASS OF NONLINEAR OPERATORS

  • Chidume, C.E.;Nnoli, B.V.C.
    • 대한수학회보
    • /
    • 제39권2호
    • /
    • pp.269-276
    • /
    • 2002
  • Let E be a real Banach space. Let T : E longrightarrow E be a map with F(T) : = { x $\in$ E : Tx = x} $\neq$ 0 and satisfying the accretive-type condition $\lambda\$\mid$x-Tx\$\mid$^2$, for all $x\inE,\;x^*\inf(T)\;and\;\lambda >0$. We prove some necessary and sufficient conditions for the convergence of the Mann iterative sequence to a fixed point of T.

WEAK CONVERGENCE OF MANN ITERATIVE SEQUENCE FOR NONEXPANSIVE MAPPINGS IN PROBABILISTIC HILBERT SPACES

  • Su, Yongfu;Wang, Xiuzhen;Gao, Junyu
    • East Asian mathematical journal
    • /
    • 제24권1호
    • /
    • pp.27-33
    • /
    • 2008
  • The purpose of this paper is to establish the weak convergence theorem of Mann iterative sequence for nonexpansive mappings in probabilistic Hilbert spaces. In order to establish the weak convergence theorem, a new method was presented in this paper, that is method of mathematical expectation.

  • PDF

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

  • Xue, Zhiqun
    • 대한수학회보
    • /
    • 제47권2호
    • /
    • pp.295-305
    • /
    • 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.

ITERATIVE APPROXIMATION OF FIXED POINTS FOR STRONGLY PSEUDO-CONTRACTIVE MAPPINGS

  • Sharma, Sushil;Deshpande, Bhavana
    • 대한수학회보
    • /
    • 제39권1호
    • /
    • pp.43-51
    • /
    • 2002
  • The aim of this paper is to prove a convergence theorem of a generalized Ishikawa iteration sequence for two multi-valued strongly pseudo-contractive mappings by using an approximation method in real uniformly smooth Banach spaces. We generalize and extend the results of Chang and Chang, Cho, Lee, Jung, and Kang.

Superior Mandelbrot Set

  • Rani, Mamta;Kumar, Vinod
    • 한국수학교육학회지시리즈D:수학교육연구
    • /
    • 제8권4호
    • /
    • pp.279-291
    • /
    • 2004
  • Mandelbrot sets and its generalizations have been extensively studied by using the Picard iterations. The purpose of this paper is to study superior Mandelbrot sets, a new class of Mandelbrot sets by introducing the Mann iterative procedure for polynomials Q$_{c}$(z) := z$^n$ + c. We generate some superior Mandelbrot sets for different values of n ($\geq$2) and these new figures are exciting and fascinating.g.

  • PDF

ON FIXED POINT OF UNIFORMLY PSEUDO-CONTRACTIVE OPERATOR AND SOLUTION OF EQUATION WITH UNIFORMLY ACCRETIVE OPERATOR

  • Xu, Yuguang;Liu, Zeqing;Kang, Shin-Min
    • East Asian mathematical journal
    • /
    • 제24권3호
    • /
    • pp.305-315
    • /
    • 2008
  • The purpose of this paper is to study the existence and uniqueness of the fixed point of uniformly pseudo-contractive operator and the solution of equation with uniformly accretive operator, and to approximate the fixed point and the solution by the Mann iterative sequence in an arbitrary Banach space or an uniformly smooth Banach space respectively. The results presented in this paper show that if X is a real Banach space and A : X $\rightarrow$ X is an uniformly accretive operator and (I-A)X is bounded then A is a mapping onto X when A is continuous or $X^*$ is uniformly convex and A is demicontinuous. Consequently, the corresponding results which depend on the assumptions that the fixed point of operator and solution of the equation are in existence are improved.

  • PDF

DEMI-CLOSED PRINCIPLE AND WEAK CONVERGENCE PROBLEMS FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

  • Chang, Shih-Sen;Cho, Yeol-Je;Haiyun Zhou
    • 대한수학회지
    • /
    • 제38권6호
    • /
    • pp.1245-1260
    • /
    • 2001
  • A demi-closed theorem and some new weak convergence theorems of iterative sequences for asymptotically nonexpansive and nonexpansive mappings in Banach spaces are obtained. The results presented in this paper improve and extend the corresponding results of [1],[8]-[10],[12],[13],[15],[16], and [18].

  • PDF

MODIFIED KRASNOSELSKI-MANN ITERATIONS FOR NONEXPANSIVE MAPPINGS IN HILBERT SPACES

  • Naidu, S.V.R.;Sangago, Mengistu-Goa
    • Journal of applied mathematics & informatics
    • /
    • 제28권3_4호
    • /
    • pp.753-762
    • /
    • 2010
  • Let K be a nonempty closed convex subset of a real Hilbert space H. Let T : K $\rightarrow$ K be a nonexpansive mapping with a nonempty fixed point set Fix(T). Let f : K $\rightarrow$ K be a contraction mapping. Let {$\alpha_n$} and {$\beta_n$} be sequences in (0, 1) such that $\lim_{x{\rightarrow}0}{\alpha}_n=0$, (0.1) $\sum_{n=0}^{\infty}\;{\alpha}_n=+{\infty}$, (0.2) 0 < a ${\leq}\;{\beta}_n\;{\leq}$ b < 1 for all $n\;{\geq}\;0$. (0.3) Then it is proved that the modified Krasnoselski-Mann iterative sequence {$x_n$} given by {$x_0\;{\in}\;K$, $y_n\;=\;{\alpha}_{n}f(x_n)+(1-\alpha_n)x_n$, $n\;{\geq}\;0$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, $n\;{\geq}\;0$, (0.4) converges strongly to a point p $\in$ Fix(T} which satisfies the variational inequality

    $\leq$ 0, z $\in$ Fix(T). (0.5) This result improves and extends the corresponding results of Yao et al[Y.Yao, H. Zhou, Y. C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J Appl Math Com-put (2009)29:383-389.