• Honam Mathematical Journal
• /
• v.43 no.3
• /
• pp.441-452
• /
• 2021

In this paper, improved power-mean integral inequality, which provides a better approach than power-mean integral inequality, is proved. Using Hölder-İşcan integral inequality and improved power-mean integral inequality, some inequalities of Hadamard's type for functions whose derivatives in absolute value at certain power are quasi-convex are given. In addition, the results obtained are compared with the previous ones. Then, it is shown that the results obtained together with identity are better than those previously obtained.

• Bulletin of the Korean Mathematical Society
• /
• v.28 no.2
• /
• pp.163-174
• /
• 1991

This is a continuation of the author's previous work [17]. In this paper, we consider mainly variational inequalities for single-valued functions. We first obtain a generalization of the variational type inequality of Juberg and Karamardian [10] and apply it to obtain strengthened versions of the Hartman-Stampacchia inequality and the Brouwer fixed point theorem. Next, we obtain fairly general versions of Browder's variational inequality [5] and its subsequent generalizations due to Brezis et al [4], Takahashk [23], Shih and Tan [19], Simons [20], and others. Finally, in this paper, we obtain a variational inequality for non-real locally convex t.v.s. which generalizes a result of Shih and Tan [19].

• Communications of the Korean Mathematical Society
• /
• v.12 no.4
• /
• pp.881-893
• /
• 1997

E. M. Silvia introduced the class $S^\lambda_\alpha$ of $\alpha$-spirallike functions f(z) satisfying the condition $$ (A) Re[(e^{i\lambda} - \alpha) \frac{zf'(z)}{f(z)} + \alpha \frac{(zf'(z))'}{f'(z)}] > 0, $$ where $\alpha \geq 0, $\mid$\lambda$\mid$ < \frac{\pi}{2}$ and $$\mid$z$\mid$ < 1$. We will generalize Silvia class of functions by formally replacing f(z) in the denominator of (A) by a spirallike function g(z). We denote the new class of functions by $Y(\alpha,\lambda)$. In this note we obtain some results for the class $Y(\alpha,\lambda)$ including integral representation formula, relations between our class $Y(\alpha,\lambda)$ and Ziegler class $Z_\lambda$, the radius of convexity problem, a few coefficient estimates and a covering theorem for the class $Y(\alpha,\lambda)$.

• Korean Institute of Interior Design Journal
• /
• v.24 no.2
• /
• pp.142-150
• /
• 2015

The purpose of this study is to analysis the change of rural house type and house plans in Bonghwa province. According to definition of rural area, the scopes of the research of rural houses limited the Bonghwa rural area(1 eup, 9 myeon). The method of study is to compare and analyze about housing situation, structure of house, housing type and construction of house space etc. through the statistical data of Bongwha statistical yearbook, space syntax(convex analysis) and other various data etc. during these 10 years. As a results of the analysis 1) According to Change of family member the supply ratio of detached house is steadily decreasing and changing from a detached house to multi-household house in Bongwha areas. 2) Most of houses structure were using lightweight steel construction because of cost-cutting of construction and easy way to construct etc.. 3) The highest Integration space is living space in rural house plans 4) The highest segregation space is bathroom space of master bed room in rural house plans. Some of bed rooms are classed as segregation space regardless of Integration space 5) Traditional front yard's function is changing from the place with the various functions to the place with the specific functions.

• Management Science and Financial Engineering
• /
• v.12 no.1
• /
• pp.113-125
• /
• 2006

Bilevel programming problem is a two-stage optimization problem where the constraint region of the first level problem is implicitly determined by another optimization problem. In this paper we consider the bilevel quadratic/linear fractional programming problem in which the objective function of the first level is quasiconcave, the objective function of the second level is linear fractional and the feasible region is a convex polyhedron. Considering the relationship between feasible solutions to the problem and bases of the coefficient submatrix associated to variables of the second level, an enumerative algorithm is proposed which finds a global optimum to the problem.

• Honam Mathematical Journal
• /
• v.42 no.2
• /
• pp.301-318
• /
• 2020

In this paper, we introduce and study the concept of hyperbolic type convexity functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for this class of functions. In addition, we obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is hyperbolic convexity. Moreover, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities.

• Journal of applied mathematics & informatics
• /
• v.26 no.1_2
• /
• pp.251-261
• /
• 2008

In this paper second order cone convex, second order cone pseudoconvex, second order strongly cone pseudoconvex and second order cone quasiconvex functions are introduced and their interrelations are discussed. Further a MondWeir Type second order dual is associated with the Vector Minimization Problem and the weak and strong duality theorems are established under these new generalized convexity assumptions.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.707-716
• /
• 2015

Some Hermite-Hadamard type inequalities for the fractional integrals are established and these results have some relationship with the obtained results of [11, 12].

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.2
• /
• pp.253-267
• /
• 2003

In this paper we deal With the quadratic functional equation (equation omitted) deriving from an inequality of T. Popoviciu for convex functions. We solve this functional equation by proving that its solutions we the polynomials of degree at most two. Likewise, we investigate its stability in the spirit of Hyers, Ulam, and Rassias.

• Journal of applied mathematics & informatics
• /
• v.16 no.1_2
• /
• pp.125-142
• /
• 2004

We analyze the convergence properties of Powell's UOBYQA method. A distinguished feature of the method is its use of two trust region radii. We first study the convergence of the method when the objective function is quadratic. We then prove that it is globally convergent for general objective functions when the second trust region radius p converges to zero. This gives a justification for the use of p as a stopping criterion. Finally, we show that a variant of this method is superlinearly convergent when the objective function is strictly convex at the solution.