• 제목/요약/키워드: Accretive operators

검색결과 35건 처리시간 0.021초

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
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    • 제39권2호
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    • pp.269-276
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    • 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.

CONVERGENCE OF AN ITERATIVE ALGORITHM FOR SYSTEMS OF GENERALIZED VARIATIONAL INEQUALITIES

  • Jeong, Jae Ug
    • Korean Journal of Mathematics
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    • 제21권3호
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    • pp.213-222
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    • 2013
  • In this paper, we introduce and consider a new system of generalized variational inequalities involving five different operators. Using the sunny nonexpansive retraction technique we suggest and analyze some new explicit iterative methods for this system of variational inequalities. We also study the convergence analysis of the new iterative method under certain mild conditions. Our results can be viewed as a refinement and improvement of the previously known results for variational inequalities.

ITERATIVE ALGORITHMS FOR A SYSTEM OF RANDOM NONLINEAR EQUATIONS WITH FUZZY MAPPINGS

  • Kim, Jong Kyu;Salahuddin, Salahuddin
    • East Asian mathematical journal
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    • 제34권3호
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    • pp.265-285
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    • 2018
  • The main purpose of this paper, by using the resolvent operator technique associated with randomly (A, ${\eta}$, m)-accretive operator is to establish an existence and convergence theorem for a class of system of random nonlinear equations with fuzzy mappings in Banach spaces. Our works are improvements and generalizations of the corresponding well-known results.

ACCRETIVE OPERATORS IN A PROBABILISITIC NORMED SPACES

  • Ha, Ki-Sik;Shin, Ki-Yeon;Cho, Yeol-Je
    • 대한수학회보
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    • 제31권1호
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    • pp.45-54
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    • 1994
  • Throughout this paper, the definitions and properities related to probabilistic normed spaces are followed as in [2]. Let R be the set of all real numbers. A mapping F:R .rarw. [0, 1] is called a distribution function on R if it is nondecreasing and left continuous with inf F = 0 and sup F = 1. We denote by L the set of all distribution functions on R.

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