• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.163-176
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• 2008

In this paper, we introduce and study a new class of generalized nonlinear variational-like inequalities. By employing the auxiliary principle technique we suggest an iterative algorithm to compute approximate solutions of the generalized nonlinear variational-like inequalities. We discuss the convergence of the iterative sequences generated by the algorithm in Banach spaces and prove the existence of solutions and convergence of the algorithm for the generalized nonlinear variational-like inequalities in Hilbert spaces, respectively. Our results extend, improve and unify several known results due to Ding, Liu et al, and Zeng, and others.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1019-1036
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• 2016

In this paper, we study the existence of solutions and $L^2$-regularity for fractional order retarded neutral functional differential equations in Hilbert spaces. We no longer require the compactness of structural operators to prove the existence of continuous solutions of the non-linear differential system, but instead we investigate the relation between the regularity of solutions of fractional order retarded neutral functional differential systems with unbounded principal operators and that of its corresponding linear system excluded by the nonlinear term. Finally, we give a simple example to which our main result can be applied.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1331-1345
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• 2016

A K-g-frame is a generalization of a g-frame. It can be used to reconstruct elements from the range of a bounded linear operator K in Hilbert spaces. K-g-frames have a certain advantage compared with g-frames in practical applications. In this paper, the interchangeability of two g-Bessel sequences with respect to a K-g-frame, which is different from a g-frame, is discussed. Several construction methods of K-g-frames are also proposed. Finally, by means of the methods and techniques in frame theory, several results of the stability of K-g-frames are obtained.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.205-235
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• 2023

In this paper, we introduce and study an iterative technique for solving quasimonotone split variational inequality problems and fixed point problem in the framework of real Hilbert spaces. Our proposed iterative technique is self adaptive, and easy to implement. We establish that the proposed iterative technique converges strongly to a minimum-norm solution of the problem and give some numerical illustrations in comparison with other methods in the literature to support our strong convergence result.

• East Asian mathematical journal
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• v.25 no.4
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• pp.415-423
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• 2009

In this paper, we consider the hybrid monotone projection algorithm for asymptotically quasi-pseudocontractive mappings. A strong convergence theorem is established in the framework of Hilbert spaces. Our results mainly improve the corresponding results announced by [H. Zhou, Demiclosedness principle with applications for asymptotically pseudo-contractions in Hilbert spaces, Nonlinear Anal. 70 (2009) 3140-3145] and also include Kim and Xu [T.H. Kim, H.K. Xu, Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140-1152; Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal. 68 (2008) 2828-2836] as special cases.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.613-622
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• 2012

In this paper, we propose a new algorithm to modify the standard Mann' process to have strong convergence for $k$-strictly pseudo-contractive non-self mapping in Hilbert spaces.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.565-575
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• 2013

Let H be a real Hilbert space and let T : H ${\rightarrow}$ H be a Lipschitz pseudocontractive mapping. We introduce a modified Ishikawa iterative algorithm and prove that if $F(T)=\{x{\in}H:Tx=x\}{\neq}{\emptyset}$, then our proposed iterative algorithm converges strongly to a fixed point of T. No compactness assumption is imposed on T and no further requirement is imposed on F(T).

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.767-786
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• 2018

In this paper, we introduce new iterative schemes by using the modified Ishikawa iteration for two hybrid multivalued mappings in a Hilbert space. We then obtain weak convergence theorem under suitable conditions. We use CQ and shrinking projection methods with Ishikawa iteration for obtaining strong convergence theorems. Furthermore, we give examples and numerical results for supporting our main results.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1263-1275
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• 2010

In this paper, we introduce a new iterative scheme for finding a common element of the set of common fixed points of infinite family of nonexpansive mappings and the set of solutions to a generalized equilibrium problem and the set of solutions to a variational inequality problem in a real Hilbert space. Then strong convergence of the scheme to a common element of the three sets is proved. As applications, three new strong convergence theorems are obtained. Our theorems extend important recent results.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.515-523
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• 2019

The aim of this paper is to present some necessary and sufficient conditions for existence of solution of Sylvester operator equation involving bounded subnormal operators in a Hilbert space. Our results improve and generalize some results in the literature involving normal operators.