S. H. Shim's research while affiliated with Gyeongsang National University and other places

Publications (4)

Article
Let K be a nonempty closed bounded convex subset of an arbitrary smooth Banach space X and T : K → K be a strictly hemi-contractive operator. Under some conditions we obtain that the Mann iteration method with errors both converges strongly to a unique fixed point of T and is almost T -stable on K. The results presented in this paper generalize the...
Article
In this paper we introduce and study a new class of generalized set-valued strongly nonlinear quasivariational inclusions. Using the resolvent operator technique for maximal monotone mapping, we construct some new iterative algorithms for solving this class of generalized set-valued strongly nonlinear quasivariational inclusion. We prove the existe...
Article
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In this paper, we introduce a new class of completely generalized strongly nonlinear implicit quasivariational inclusions and prove its equivalence with a class of fixed point problems by using some properties of maximal monotone mappings. We also prove the existence of solutions for the completely generalized strongly nonlinear implicit quasivaria...
Article
We study a class of generalized strongly nonlinear implicit quasi-variational inequality problems for fuzzy mappings and prove that the generalized strongly nonlinear implicit quasi-variational inequality problem for fuzzy mappings is equivalent to solving the fixed point problem. Using this quivalence, a new iterative algorithm for finding the app...

Citations

... Motivated and inspired by the recent research works in these fascinating areas, the random variational inequality problems, random quasi- variational inequality problems, random variational inclusion problems and random quasi- complementarity problems have been introduced and studied by Ahmad and Bazán 16, Chang 17, Chang and Huang 18, Cho et al. 19, Ganguly and Wadhwa 20, Huang 21, Huang and Cho 22, Huang et al. 23, and Noor and Elsanousi 24. Inspired and motivated by recent works in these fields see 3,11,12,16,[25][26][27][28], in this paper, we introduce and study a new class of general nonlinear random multivalued operator equations involving generalized m-accretive mappings in Banach spaces. By using the Chang's lemma and the resolvent operator technique for generalized m-accretive mapping due to Huang and Fang 15, we also prove the existence theorems of the solution and convergence theorems of the generalized random iterative procedures with errors for this nonlinear random multivalued operator equations in q-uniformly smooth Banach spaces. ...
... With the emergence of probabilistics functional analysis, the study of random operators became a central topic of this discipline [4,5]. The theory of resolvent operators introduced by Brezis [2] is closely related to the variational inequality problems; for applications we refer to678. Motivated by recent research work on random variational inequalities91011121314, in this paper we consider a class of set valued nonlinear random implicit quasi variational inclusions and a class of random proximal operator equations and establish an equivalence between them. ...
... Application of strictly hemicontractive-type mapping was initiated by Chidume and Osilike [4] for improving the consequence of Chidume [5]. After Chidume and Osilike [4], several researchers studied strictly hemicontractive-type mapping in many directions; see for instance [1][2][3][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and the references cited therein. Among the articles cited in [1][2][3][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], Hussain et al. [1] studied Lipschitz strictly hemicontractive-type mapping in arbitrary Banach spaces to extend and improve the equivalent consequences of the monographs [4,5,[12][13][14][15]. ...
... , v, w ∈ H for i ∈ {1, 2}, then the problem 2.13 reduces to finding x ∈ H such that0 ∈ N Ax, Bx M x, f − g x , 2.15which was studied in Shim et al.19 .It is easy to see that the problem 2.13 includes a number of variational and variational-like inclusions as special cases for appropriate and suitable choice of the mappings N i , A i , B i , C i , M i , f i , g i for i ∈ {1, 2}. ...