• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.609-624
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• 1996

Recently, Giannessi [9] firstly introduced the vector-valued variational inequalities in a real Euclidean space. Later Chen et al. [5] intensively discussed vector-valued variational inequalities and vector-valued quasi variationl inequalities in Banach spaces. They [4-8] proved some existence theorems for the solutions of vector-valued variational inequalities and vector-valued quasi-variational inequalities. Lee et al. [14] established the existence theorem for the solutions of vector-valued variational inequalities for multifunctions in reflexive Banach spaces.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1381-1395
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• 2009

Mixed type second order dual to the non-differentiable problem containing support functions is formulated and duality theorems are proved under generalized second order convexity conditions. It is pointed out that the mixed type duality results already reported in the literature are the special cases of our results.

• Communications of the Korean Mathematical Society
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• v.24 no.4
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• pp.523-528
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• 2009

In this paper, we consider the existence of solutions to some generalized vector quasi-equilibrium-like problem under a c-diagonal quasi-convexity assumptions, but not monotone concepts. For an example, in the proof of Theorem 1, the c-diagonally quasi-convex concepts of a set-valued mapping was used but monotone condition was not used. Our problem is a new kind of equilibrium problems, which can be compared with those of Hou et al. [4].

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.91-103
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• 2021

In this paper we have established inequalities for a unified integral operator by using convexity of composition of two functions. The obtained results are directly connected to bounds of various fractional and conformable integral operators which are already known in literature. A generalized Hadamard integral inequality is obtained which further leads to its various versions for associated fractional integrals. Further, some implicated results are discussed.

• Korean Journal of Mathematics
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• v.32 no.1
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• pp.73-82
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• 2024

The purpose of this paper is to introduce a new subclass of strongly meromorphic close-to-convex functions by subordinating to generalized Janowski function. We investigate several properties for this class such as coefficient estimates, inclusion relationship, distortion property, argument property and radius of meromorphic convexity. Various earlier known results follow as particular cases.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.517-526
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• 2024

In this paper, some iterative methods are used to discuss the behavior of general mixed-harmonic variational inequalities. We employ the auxiliary principle technique and g-strongly harmonic monotonicity of the operator to obtain results on the existence of solutions to a generalized class of mixed harmonic variational inequality.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.587-592
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• 1996

In 1950, Nash [5] first proved the existence of equilibrium for games where the player's preferences are representable by continuous quasiconcave utilities and the strategy sets are simplexes. Next Debreu [3] proved the existence of equilibrium for abstract economies. Recently, the existence of Nash equilibrium can be further generalized in more general settings by several athors, e.g. Shafer-Sonnenschein [6], Borglin-Keiding [2], Yannelis-Prabhaker [8]. In the above results, the convexity assumption is very essential and the main proving tools are the continuous selection technique and the existence of maximal elements. Still there have been a number of generalizations and applications of equilibrium existence theorem in generalized games.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.683-695
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• 2001

In this paper we are concerned with theoretical properties of gap functions for the extended variational inequality problem (EVI) in a general Banach space. We will present a correction of a recent result of Chen et. al. without assuming the convexity of the given function Ω. Using this correction, we will discuss the continuity and the differentiability of a gap function, and compute its gradient formula under tow particular situations in a general Banach space. Our results can be regarded as infinite dimensional generalizations of the well-known results of Fukushima, and Zhu and Marcotte with soem modifications.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.287-301
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• 2014

In this paper, we prove a necessary optimality theorem for a nonsmooth optimization problem in the face of data uncertainty, which is called a robust optimization problem. Recently, the robust optimization problems have been intensively studied by many authors. Moreover, we give examples showing that the convexity of the uncertain sets and the concavity of the constraint functions are essential in the optimality theorem. We present an example illustrating that our main assumptions in the optimality theorem can be weakened.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.397-410
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• 2007

Visualization of 2D and 3D data, which arises from some scientific phenomena, physical model or mathematical formula, in the form of curve or surface view is one of the important topics in Computer Graphics. The problem gets critically important when data possesses some inherent shape feature. For example, it may have positive feature in one instance and monotone in the other. This paper is concerned with the solution of similar problems when data has convex shape and its visualization is required to have similar inherent features to that of data. A rational cubic function [5] has been used for the review of visualization of 2D data. After that it has been generalized for the visualization of 3D data. Moreover, simple sufficient constraints are made on the free parameters in the description of rational bicubic functions to visualize the 3D convex data in the view of convex surfaces.