• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1371-1379
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• 2009

In this paper, we introduce a relaxed hybrid-type$\eta$-f-${\alpha}$-pseudomo-notonicity. By using the KKM-technique, we establish some existence results for set-valued variational-like inequalities with $\eta-f-\alpha$-pseudomonotone, relaxed $\eta-f-\alpha$-pseudomonotone, Fan-KKM Theorem.

• East Asian mathematical journal
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• v.25 no.2
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• pp.159-169
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• 2009

In this paper, we introduce a generalized system of nonlinear relaxed co-coercive variational inclusions involving (A, ${\eta}$)-monotone map-pings in the framework of Hilbert spaces. Based on the generalized resol-vent operator technique associated with (A, ${\eta}$)-monotonicity, we consider the approximation solvability of solutions to the generalized system. Since (A, ${\eta}$)-monotonicity generalizes A-monotonicity and H-monotonicity, The results presented this paper improve and extend the corresponding results announced by many others.

• Journal of the Korean Society for Nondestructive Testing
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• v.20 no.5
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• pp.438-444
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• 2000

The prediction of mechanical properties for WC-Co alloys by evaluation of coercive force and magnetic saturation were studied in relation to their microstructure. The WC-8%Co alloys were prepared using different WC particle size, carbon content and various sintering temperature by PM process. The magnetic properties such as coercive force and magnetic saturation of sintered WC-Co alloys were critically dependent upon their final composition and microstructure. Slight changes of carbon contents and small variation of WC grain size result in marked changes of magnetic properties, hardness and transverse rupture strength of sintered WC-Co alloys. It was found that the coercive force and hardness were increased by fine WC grain size of sinterd alloys, and the coercive force was proportional to hardness. With decreasing total carbon content below the stoichiometric value in WC-8%Co alloys the volume fraction of $\eta$ phase increased steadily, while the magnetic saturation and transverse rupture strength decreased. The magnetic saturation was inversely proportional to the coercive force of WC-Co alloys.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1323-1339
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• 2008

In this paper, a new class of $(h,{\eta})$-proximal for proper functionals in Hilbert spaces is introduced. The existence and Lip-schitz continuity of the $(h,{\eta})$-proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonlinear quasi-variational-like inclusion is suggested. The existence and uniqueness theorems of solution for the generalized nonlinear quasi-variational-like inclusion are established. The convergence and stability results of iterative sequence generated by the perturbed three-step iterative algorithm with errors are discussed.