• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.743-756
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• 2022

We obtained results on upper hemi-continuous and pseudo-monotone type two mappings for sets which are not compact. M.S.R. Chowdhury and K.-K. Tan's improved result on Ky Fan's minimax inequality will be used.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.933-957
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• 2017

In this paper, we prove some existence results of solutions for a new class of generalized bi-quasi-variational-like inequalities (GBQVLI) for (${\eta}-h$)-quasi-pseudo-monotone type I and strongly (${\eta}-h$)-quasi-pseudo-monotone type I operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. To obtain our results on GBQVLI for (${\eta}-h$)-quasi-pseudo-monotone type I and strongly (${\eta}-h$)-quasi-pseudo-monotone type I operators, we use Chowdhury and Tan's generalized version of Ky Fan's minimax inequality as the main tool.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.763-771
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• 2009

T.H. Kim, H.K. Xu, [Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal.(2007),doi:l0.l016/j.na.2007.02.029.] proved the strong convergence for asymptotically strict pseudo-contractions by the classical CQ iterative method. In this paper, we apply the monotone CQ iterative method to modify the classical CQ iterative method of T.H. Kim, H.K. Xu, and to obtain the strong convergence theorems for asymptotically strict pseudo-contractions. In the proved process of this paper, Cauchy sequences method is used, so we complete the proof without using the demi-closedness principle, Opial's condition or others about weak topological technologies. In addition, we use a ingenious technology to avoid defining that F(T) is bounded. On the other hand, we relax the restriction on the control sequence of iterative scheme.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.621-640
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• 2014

In this paper, we introduce a new approximating method for finding the common element of the set of fixed points of nonexpansive mappings and the set of solution of system variational inequalities for finite family of inverse strongly monotone mappings and strictly pseudo-contractive of Browder-Petryshyn type mappings. We show that the sequence converges strongly to a common element the above two sets under some parameter controling conditions. Our results improve and extend the results announced by many others.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.757-777
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• 2019

In this paper, we study the convergence analysis of the sequences generated by the proximal point method for an infinite family of pseudo-monotone equilibrium problems in Banach spaces. We first prove the weak convergence of the generated sequence to a common solution of the infinite family of equilibrium problems with summable errors. Then, we show the strong convergence of the generated sequence to a common equilibrium point by some various additional assumptions. We also consider two variants for which we establish the strong convergence without any additional assumption. For both of them, each iteration consists of a proximal step followed by a computationally inexpensive step which ensures the strong convergence of the generated sequence. Also, for this two variants we are able to characterize the strong limit of the sequence: for the first variant it is the solution lying closest to an arbitrarily selected point, and for the second one it is the solution of the problem which lies closest to the initial iterate. Finally, we give a concrete example where the main results can be applied.

• 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 the Korean Mathematical Society
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• v.33 no.2
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• pp.291-307
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• 1996

In this paper, we shall show the existence of solutions of the following nonlinear partial differential equation $$ {^{divA(-\Delta u) = f(x, u, \Delta u) in \Omega}^{u = 0 on \partial\Omega} $$ where $f(x, u, \Delta u) = -u$\mid$\Delta u$\mid$^{p-2} + h, p \geq 2, h \in L^\infty$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.3C
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• pp.271-280
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• 2008

M channel near-perfect-reconstruction(NPR) pseudo-QMF banks are a hybrid of conventional pseudo-QMF design and spectral factorization approach where the analysis and synthesis filters are cosine-modulated versions of the prototype-lowpass filter(p-LPF). However, p-LPF H(z) does not have linear-phase symmetry as well as magnitude-distortion optimization since it is obtained by spectral factorization of $2M^{-th}$ band filter $G(z)=z^{-(N-1)}H(z^{-1})H(z)$. A fair amount of attention, therefore, has been focused on the design of filter banks for reducing only alias-cancellation distortion without reconstructed-amplitude distortion. In this paper, we propose a new method for designing linear-phase p-LPF in NPR pseudo-QMF banks, which is based on Maxflat(maximally flat) FIR filters with closed-form transfer function. In addition, p-LPF H(z) is optimized in this approach so that the 2M-channel overall distortion response represented with $G(z)=H^2(z)$ approximately becomes an unit magnitude response. Through several examples of NPR pseudo-QMF banks, it is shown that the peek ripple of the overall magnitude distortion is less than $3.5{\times}10^{-4}\;({\simeq}-70dB)$ and analysis/synthesis filters have the sharp monotone-stopband attenuation exceeding 100 dB.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.23-44
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• 2022

In this paper, we consider and introduce some new concepts of the biconvex functions involving an arbitrary bifunction and function. Some new relationships among various concepts of biconvex functions have been established. We have shown that the optimality conditions for the general biconvex functions can be characterized by a class of bivariational-like inequalities. Auxiliary principle technique is used to propose proximal point methods for solving general bivariational-like inequalities. We also discussed the conversance criteria for the suggested methods under pseudo-monotonicity. Our method of proof is very simple compared with methods. Several special cases are discussed as applications of our main concepts and results. It is a challenging problem to explore the applications of the general bivariational-like inequalities in pure and applied sciences.