• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1395-1408
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• 2010

In this paper, a pair of Wolfe type second-order nondifferentiable multiobjective symmetric dual program over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under second-order (F, $\alpha$, $\rho$, d)-convexity assumptions. An illustration is given to show that second-order (F, $\alpha$, $\rho$, d)-convex functions are generalization of second-order F-convex functions. Several known results including many recent works are obtained as special cases.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.797-804
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• 1998

A pair of multiobjective generalized symmetric dual non-linear programming problems and weak strong and converse dual-ity theorems for these problems are established under generalized $\rho-(\eta,0)$-invexity assumptions. Several known results are obtained as special cases.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.401-415
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• 2015

In this paper, we propose a modified proximal point algorithm which consists of a resolvent operator technique step followed by a generalized projection onto a moving half-space for approximating a solution of a variational inclusion involving a maximal monotone mapping and a monotone, bounded and continuous operator in Banach spaces. The weak convergence of the iterative sequence generated by the algorithm is also proved.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.153-169
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• 2000

Let E be a real q-uniformly smooth Banach space which admits a weakly sequentially continuous duality map, and K a nonempty closed convex subset of E. Let T : K -> K be a mapping such that $F(T)\;=\;{x\;{\in}\;K\;:\;Tx\;=\;x}\;{\neq}\;0$ and (I - T) satisfies the accretive-type condition: $\;{\geq}\;{\lambda}$\mid$$\mid$x-Tx$\mid$$\mid$^2$, for all $x\;{\in}\;K,\;x^*\;{\in}\;F(T)$ and for some ${\lambda}\;>\;0$. The weak and strong convergence of the Ishikawa iteration method to a fixed point of T are investigated. An application of our results to the approximation of a solution of a certain linear operator equation is also given. Our results extend several important known results from the Mann iteration method to the Ishikawa iteration method. In particular, our results resolve in the affirmative an open problem posed by Naimpally and Singh (J. Math. Anal. Appl. 96 (1983), 437-446).

• The Journal of the Korea Contents Association
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• v.6 no.5
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• pp.29-34
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• 2006

For the almost certainly convergent series $S_n=\sum_{i=1}^nV-i$ of independent random elements in Banach spaces, by investigating tail series laws of large numbers, the rate of convergence of the series $S_n$ to a random variable s is studied in this paper. More specifically, by studying the duality between the limiting behavior of the tail series $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}V-i$ of random variables and that of Banach space valued random elements, an alternative way of proving a result of the previous work, which establishes the equivalence between the tail series weak law of large numbers and a limit law, is provided in a Banach space setting.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.835-852
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• 2013

In this paper, we have considered a class of constrained non-smooth multiobjective fractional programming problem involving support functions under generalized convexity. Also, second order Mond Weir type dual and Schaible type dual are discussed and various weak, strong and strict converse duality results are derived under generalized class of second order (F, ${\alpha}$, ${\rho}$, $d$)-V-type I functions. Also, we have illustrated through non-trivial examples that class of second order (F, ${\alpha}$, ${\rho}$, $d$)-V-type I functions extends the definitions of generalized convexity appeared in the literature.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.103-127
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• 2018

This paper is dedicated to studying some Hausdorff operators on the Heisenberg group ${\mathbb{H}}^n$. The sharp bounds on the strong-type weighted Lorentz spaces ${\Lambda}^p_u(w)$ and the weak-type weighted Lorentz spaces ${\Lambda}^{p,{\infty}}_u(w)$ are investigated. Especially, the results cover the classical power weighted space $L^{p,q}_{\alpha}$. The results are also extended to the product spaces ${\Lambda}^{p_1}_{u_1}(w_1){\times}{\Lambda}^{p_2}_{u_2}(w_2)$, especially for $L^{p_1,q_1}_{{\alpha}_1}{\times}L^{p_2,q_2}_{{\alpha}_2}$. Our proofs are quite different from those in previous documents since the duality principle, and some well-known inequalities concerning the weights are adopted. The results recover the existing results as well as we obtain new results in the new and old settings.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.185-190
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• 2005

For the almost certainly convergent series $S_n$ of independent random variables the limiting behavior of tail series ${T_n}{\equiv}S-S_{n-1}$ is reviewed. More specifically, tail series strong laws of large number and tail series weak laws of large numbers will be introduced, and their relationship will be investigated. Then, the relationship will also be extended to the case of Banach space valued random elements, by investigating the duality between the limiting behavior of the tail series of random variables and that of random elements.

• The KIPS Transactions:PartD
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• v.14D no.1 s.111
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• pp.121-130
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• 2007

in a software development, the design or architecture prior to implementing the software is essential for the success. This paper presents a case that we successfully designed a software architecture of radiation monitoring system (RMS) for HANARO research reactor currently operating in KAERI by applying the quality attribute-driven design method which is modified from the attribute-driven design (ADD) introduced by Bass[1]. The quality attribute-driven design method consists of following procedures: eliciting functionality and quality requirements of system as architecture drivers, selecting tactics to satisfy the drivers, determining architectures based on the tactics, and implementing and validating the architectures. The availability, maintainability, and interchangeability were elicited as duality requirements, hot-standby dual servers and weak-coupled modulization were selected as tactics, and client-server structure and object-oriented data processing structure were determined at architectures for the RMS. The architecture was implemented using Adroit which is a commercial off-the-shelf software tool and was validated based on performing the function-oriented testing. We found that the design method in this paper is an efficient method for a project which has constraints such as low budget and short period of development time. The architecture will be reused for the development of other RMS in KAERI. Further works are necessary to quantitatively evaluate the architecture.