• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.129-137
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• 2010

In this paper, we introduce and study a system of nonlinear set-valued implicit variational inclusions (SNSIVI) with relaxed cocoercive mappings in real Banach spaces. By using resolvent operator technique for M-accretive mapping, we construct a new class of iterative algorithms for solving this class of system of set-valued implicit variational inclusions. The convergence of iterative algorithms is proved in q-uniformly smooth Banach spaces. Our results generalize and improve the corresponding results of recent works.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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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.

• East Asian mathematical journal
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• v.26 no.5
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• pp.681-691
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• 2010

A system of variational inclusions with (A, ${\eta}$, m)-accretive operators in real q-uniformly smooth Banach spaces is introduced. Using the resolvent operator technique associated with (A, ${\eta}$, m)-accretive operators, we prove the existence and uniqueness of solutions for this system of variational inclusions and propose a Mann type iterative algorithm for approximating the unique solution for the system of variational inclusions.

• The Pure and Applied Mathematics
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• v.11 no.4
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• pp.293-308
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• 2004

Let K be a nonempty convex subset of an arbitrary Banach space X and $T\;:\;K\;{\rightarrow}\;K$ be a uniformly continuous strictly hemi-contractive operator with bounded range. We prove that certain Ishikawa iteration scheme with errors both converges strongly to a unique fixed point of T and is almost T-stable on K. We also establish similar convergence and almost stability results for strictly hemi-contractive operator $T\;:\;K\;{\rightarrow}\;K$, where K is a nonempty convex subset of arbitrary uniformly smooth Banach space X. The convergence results presented in this paper extend, improve and unify the corresponding results in Chang [1], Chang, Cho, Lee & Kang [2], Chidume [3, 4, 5, 6, 7, 8], Chidume & Osilike [9, 10, 11, 12], Liu [19], Schu [25], Tan & Xu [26], Xu [28], Zhou [29], Zhou & Jia [30] and others.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.255-275
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• 2022

In this paper, we introduce a new system of set-valued variational inclusion problems in semi-inner product spaces. We use resolvent operator technique to propose an iterative algorithm for computing the approximate solution of the system of set-valued variational inclusion problems. The results presented in this paper generalize, improve and unify many previously known results in the literature.

• Journal of applied mathematics & informatics
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• v.3 no.1
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• pp.47-54
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• 1996

We prove that if RUC(S) has a left invariant mean ${\rho}={T_{S} : s \;{\in}\; S}$ is a continuous repesentation of S as nonexpansive map-pings on a closed convex subset C of a p-uniformly convex and p-uniformly smooth Banach space and C contains an element of bounded orbit then C contains a common fixed point for ${\rho}$.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.105-118
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• 2010

The purpose of this paper is to consider an iterative method for an equilibrium problem and a family relatively nonexpansive mappings. Weak convergence theorems are established in uniformly smooth and uniformly convex Banach spaces.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.329-341
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• 2005

In this paper, we introduce new random iterative sequences with errors approximating a unique random common fixed point for three random set-valued strongly pseudo-contractive mappings and show the convergence of the random iterative sequences with errors by using an approximation method in real uniformly smooth separable Banach spaces. As applications, we study the existence of random solutions for some kind of random nonlinear operator equations group in separable Hilbert spaces.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1023-1036
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• 2015

Let {Xn; $n{\succeq}1$} be a field of martingale differences taking values in a p-uniformly smooth Banach space. The paper provides conditions under which the series ${\sum}_{i{\preceq}n}\;Xi$ converges almost surely and the tail series {$Tn={\sum}_{i{\gg}n}\;X_i;n{\succeq}1$} satisfies $sup_{k{\succeq}n}{\parallel}T_k{\parallel}=\mathcal{O}p(b_n)$ and ${\frac{sup_{k{\succeq}n}{\parallel}T_k{\parallel}}{B_n}}{\rightarrow\limits^p}0$ for given fields of positive numbers {bn} and {Bn}. This result generalizes results of A. Rosalsky, J. Rosenblatt [7], [8] and S. H. Sung, A. I. Volodin [11].

• East Asian mathematical journal
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• v.26 no.5
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• pp.703-714
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• 2010

A new class of nonlinear set-valued mixed variational inclusions involving (A, ${\eta}$)-accretive mappings in Banach spaces is introduced and studied, which includes many kind of variational inclusion (inequality) and complementarity problems as special cases. By using the resolvent operator associated with (A, ${\eta}$)-accretive operator due to Lan-Cho-Verma, the existence of solution for this kind of variational inclusion is proved, and a new hybrid proximal point algorithm is established and suggested, the convergence and stability theorems of iterative sequences generated by new iterative algorithms are also given in q-uniformly smooth Banach spaces.