• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.325-331
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• 2007

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm associated with the general line search model. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the new quasi-Newton iteration equation $B_{k+1}s_k=y^*_k,\;where\;y^*_k$ is the sum of $y_k\;and\;A_ks_k,\;and\;A_k$ is some matrix. The global convergence properties of the algorithm associating with the general form of line search is proved.

• 대한수학회지
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• 제45권1호
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• pp.29-40
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• 2008

In this paper, we introduce a modified three-step iteration scheme with errors for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. We then use this scheme to approximate a common fixed point of these mappings. The results obtained in this paper extend and improve the recent ones announced by Khan, Fukhar-ud-di, Zhou, Cho, Noor and some others.

• 호남수학학술지
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• 제37권4호
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• pp.513-527
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• 2015

In this paper, we first introduce and study new concepts of ($k_1,{\cdots},k_n$)-convexity and k-segment. Secondly, we shall discuss some properties of nonisotropically starlike domains in $\mathbb{R}^n$ with respect to the origin.

• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.243-255
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• 2018

We introduce several k-uniformly subclasses of p-valent functions defined by the generalized fractional differintegral operator and investigate various inclusion relationships for these subclasses. Some interesting applications involving certain classes of integral operators are also considered.

• East Asian mathematical journal
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• 제17권2호
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• pp.175-183
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• 2001

The main object of this paper is to investigate several majorization problems involving two subclasses $S_{p,q}(\gamma)$ and $C_{p,q}(\gamma)$ of p-valently starlike and p-valently convex functions of complex order ${\gamma}{\neq}0$ in the open unit disk $\mathbb{u}$. Relevant connections of the results presented here with those given by earlier workers on the subject are also indicated.

• Kyungpook Mathematical Journal
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• 제31권2호
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• pp.235-241
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• 1991

• 충청수학회지
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• 제28권1호
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• pp.145-150
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• 2015

Aussel et al. [1] introduced the notion of inverse quasi-variational inequalities (IQVI) by combining quasi-variational inequalities and inverse variational inequalities. Discussions are made in a finite dimensional Euclidean space. In this note, we develop an infinite dimensional version of IQVI by investigating some basic properties of the regularized gap function of IQVI in a Banach space.

• 대한수학회보
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• 제38권3호
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• pp.565-573
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• 2001

In this paper, we first rove the strict quasi-concavity of maximizing function, and next prove a new maximum theorem using Fan’s generalization of the classical KKM theorem. Also an existence theorem of social equilibrium can be proved when an additional assumption on the constraint correspondence is assumed. Finally, we give illustrative two examples of constrained optimization problems.

• Kyungpook Mathematical Journal
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• 제55권3호
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• pp.679-688
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• 2015

In this paper, we obtain Fekete-$Szeg{\ddot{o}}$ inequalities for certain subclasses of analytic univalent functions of complex order associated with quasi-subordination.

• 충청수학회지
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• 제20권1호
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• pp.59-64
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• 2007

In this paper, we will introduce the generalized operator equlibrium problem and generalized operator quasi-equlibrium problem which generalize operator equlibrium problem due to Kazmi and Raouf into multi-valued and quasi-equlibrium problems. Using a Park's fixed point theorem, we will prove a new existence theorem on generalized operator equlibrium problem which serves as a basic existence theorem for various kinds of nonlinear problems.