• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.693-702
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• 2009

In this paper, we introduce and study a system of mixed variational inequalities in Banach spaces. By using J-proximal mapping and its Lipschitz continuity for a nonconvex, lower semicontinuous, subdifferentiable, proper functional, an iterative algorithm for computing the approximate solutions of system of mixed variational inequalities is suggested and analyzed. The convergence criteria of the iterative sequences generated by iterative algorithm is also discussed.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.147-155
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• 2008

In this paper, we consider proximal point algorithms based on ($A,{\eta}$)-monotone mappings in the framework of Hilbert spaces. Since ($A,{\eta}$)-monotone mappings generalize A-monotone mappings, H-monotone mappings and many other mappings, our results improve and extend the recent ones announced by [R.U. Verma, Rockafellars celebrated theorem based on A-maximal monotonicity design, Appl. Math. Lett. 21 (2008), 355-360] and [ R.T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optim. 14 (1976) 877-898] and some others.

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.717-731
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• 2021

In this paper, we introduce and study a new class of random generalized nonlinear implicit variational-like inclusion with random fuzzy mappings in a real separable Hilbert space and give its fixed point formulation. Using the fixed point formulation and the proximal mapping technique for strongly maximal monotone mapping, we suggest and analyze a random iterative scheme for finding the approximate solution of this class of inclusion. Further, we prove the existence of solution and discuss the convergence analysis of iterative scheme of this class of inclusion. Our results in this paper improve and generalize several known results in the literature.

• Asian-Australasian Journal of Animal Sciences
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• v.25 no.1
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• pp.17-21
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• 2012

The purpose of this study was to improve mapping power and resolution for the QTL influencing carcass quality in Hanwoo, which was previously detected on the bovine chromosome (BTA) 6. A sample of 427 steers were chosen, which were the progeny from 45 Korean proven sires in the Hanwoo Improvement Center, Seosan, Korea. The samples were genotyped with the set of 2,535 SNPs on BTA6 that were imbedded in the Illumina bovine 50 k chip. A linkage disequilibrium variance component mapping (LDVCM) method, which exploited both linkage between sires and their steers and population-wide linkage disequilibrium, was applied to detect QTL for four carcass quality traits. Fifteen QTL were detected at 0.1% comparison-wise level, for which five, three, five, and two QTL were associated with carcass weight (CWT), backfat thickness (BFT), longissimus dorsi muscle area (LMA), and marbling score (Marb), respectively. The number of QTL was greater compared with our previous results, in which twelve QTL for carcass quality were detected on the BTA6 in the same population by applying other linkage disequilibrium mapping approaches. One QTL for LMA was detected on the distal region (110,285,672 to 110,633,096 bp) with the most significant evidence for linkage (p< $10^{-5}$). Another QTL that was detected on the proximal region (33,596,515 to 33,897,434 bp) was pleiotrophic, i.e. influencing CWT, BFT, and LMA. Our results suggest that the LDVCM is a good alternative method for QTL fine-mapping in detection and characterization of QTL.