• Journal of applied mathematics & informatics
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• 제8권3호
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• pp.1027-1033
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• 2001

In this paper we obtain the necessary and sufficient conditions for convergence concerning the Mann iterative sequences with errors for the class of continuous accretive operators in smooth Banach spaces.

• 대한수학회지
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• 제35권1호
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• pp.191-205
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• 1998

In this paper, we prove that the Mann and Ishikawa iteration sequences with errors converge strongly to the unique solution of the equation x + Tx = f, where T is an m-accretive operator in uniformly smooth Banach spaces. Our results extend and improve those of Chidume, Ding, Zhu and others.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.261-275
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• 2002

Let T be a local strongly accretive operator from a real uniformly smooth Banach space X into itself. It is proved that Ishikawa iterative schemes with errors converge strongly to a unique solution of the equations T$\_$x/ = f and x + T$\_$x/ = f, respectively, and are almost T$\_$b/-stable. The related results deal with the strong convergence and almost T$\_$b/-stability of Ishikawa iterative schemes with errors for local strongly pseudocontractive operators.

• 대한수학회지
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• 제46권6호
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• pp.1319-1338
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• 2009

In this paper, using proximal-point mappings technique of Raccretive mappings and the property of the fixed point set of set-valued contractive mappings, we study the behavior and sensitivity analysis of the solution set of the system of parametric generalized quasi-variational inclusions involving R-accretive mappings in real uniformly smooth Banach space. Further under suitable conditions, we discuss the Lipschitz continuity of the solution set with respect to parameters. The technique and results presented in this paper can be viewed as extension of the techniques and corresponding results given in [3, 23, 24, 32, 33, 34].

• Korean Journal of Mathematics
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• 제25권1호
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• pp.19-35
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• 2017

In this communication, we introduce an Ishikawa type iterative algorithm for finding the approximate solutions of a class of nonlinear set valued variational inclusion problems. We also establish a characterization of strong convergence of this iterative techniques.

• 대한수학회지
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• 제36권6호
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• pp.1061-1073
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• 1999

Let X be a real normed linear space. Let T : D(T) ⊂ X \longrightarrow X be a uniformly continuous and ∮-strongly quasi-accretive mapping. Let {${\alpha}$n}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} , {${\beta}$n}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} be two real sequences in [0, 1] satisfying the following conditions: (ⅰ) ${\alpha}$n \longrightarrow0, ${\beta}$n \longrightarrow0, as n \longrightarrow$\infty$ (ⅱ) {{{{ SUM from { { n}=0} to inf }}}} ${\alpha}$=$\infty$. Set Sx=x-Tx for all x $\in$D(T). Assume that {u}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} and {v}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} are two sequences in D(T) satisfying {{{{ SUM from { { n}=0} to inf }}}}∥un∥<$\infty$ and vn\longrightarrow0 as n\longrightarrow$\infty$. Suppose that, for any given x0$\in$X, the Ishikawa type iteration sequence {xn}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} with errors defined by (IS)1 xn+1=(1-${\alpha}$n)xn+${\alpha}$nSyn+un, yn=(1-${\beta}$n)x+${\beta}$nSxn+vn for all n=0, 1, 2 … is well-defined. we prove that {xn}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} converges strongly to the unique zero of T if and only if {Syn}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} is bounded. Several related results deal with iterative approximations of fixed points of ∮-hemicontractions by the ishikawa iteration with errors in a normed linear space. Certain conditions on the iterative parameters {${\alpha}$n}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} , {${\beta}$n}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} and t are also given which guarantee the strong convergence of the iteration processes.

• 대한수학회지
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• 제31권3호
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• pp.333-337
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• 1994

Many authors[3][4][5] constructed and examined some processes for the fixed point of strictly pseudocontractive mapping in various Banach spaces. In fact the fixed point of strictly pseudocontractive mapping is the zero of strongly accretive operators. So the same processes are used for the both circumstances. Reich[3] proved that Mann-iteration precess can be applied to approximate the zero of strongly accretive operator in uniformly smooth Banach spaces. In the above paper he asked whether the fact can be extended to other Banach spaces the duals of which are not necessarily uniformly convex. Recently Schu[4] proved it for uniformly continuous strictly pseudocontractive mappings in smooth Banach spaces. In this paper we proved that Mann-iteration process can be applied to approximate the fixed point of strictly pseudocontractive mapping in certain Banach spaces.

• 대한수학회보
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• 제39권1호
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• pp.43-51
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• 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.

• Journal of applied mathematics & informatics
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• 제33권1_2호
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• pp.13-31
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• 2015

In this paper, we introduce a general iterative algorithm for finding a common element of the common fixed point set of an infinite family of ${\lambda}_i$-strict pseudo-contractions and the solution set of a general system of variational inclusions for two inverse strongly accretive operators in q-uniformly smooth Banach spaces. Then, we analyze the strong convergence of the iterative sequence generated by the proposed iterative algorithm under mild conditions.

• Korean Journal of Mathematics
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• 제23권3호
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• pp.409-425
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• 2015

In this paper, a new iterative scheme based on the extra-gradient-like method for finding a common element of the set of fixed points of a finite family of nonexpansive mappings and the set of solutions of modified variational inequalities in Banach spaces. A strong convergence theorem for this iterative scheme in Banach spaces is established. Our results extend recent results announced by many others.