• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.371-384
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• 2005

Usual symmetric duality results are proved for Wolfe and Mond-Weir type nondifferentiable nonlinear symmetric dual programs under F-convexity F-concavity and F-pseudoconvexity F-pseudoconcavity assumptions. These duality results are then used to formulate Wolfe and Mond-Weir type nondifferentiable minimax mixed integer dual programs and symmetric duality theorems are established. Moreover, nondifferentiable fractional symmetric dual programs are studied by using the above programs.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.147-163
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• 2017

In this paper, we establish the necessary and sufficient Karush-Kuhn-Tucker (KKT) conditions for an optimization problem with difference of set-valued maps under generalized cone convexity assumptions. We also study the duality results of Mond-Weir (MW D), Wolfe (W D) and mixed (Mix D) types for the weak solutions of the problem (P).

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.251-256
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• 2008

In this paper, we introduce the concept of the semi-preconvex set on preconvexity spaces. We study some properties for the semi-preconvex set. Also we introduce the concepts of the sc-convex function and $s^*c$-convex function. Finally, we characterize sc-convex functions, $s^*$-convex functions and semi-preconvex sets by using the co-convexity hull and the convexity hull.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.361-376
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• 2005

Optimality conditions are derived for a nonlinear fractional program in which a support function appears in the numerator and denominator of the objective function as well as in each constraint function. As an application of these optimality conditions, a dual to this program is formulated and various duality results are established under generalized convexity. Several known results are deduced as special cases.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.33-47
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• 2012

In this paper, the log-convexity of another class one-parameter mean is investigated. As applications, some new upper and lower bounds of logarithmic mean, new estimations for identric mean and new inequalities for power-exponential mean and exponential-geometric mean are first given.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.719-731
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• 2020

In this article, we find some sufficient conditions under which the modified Lommel function is close-to-convex with respect to - log(1 - z) and ${\frac{1}{2}}\;{\log}\;\({\frac{1+z}{1-z}}\)$. Starlikeness, convexity and uniformly close-to-convexity of the modified Lommel function are also discussed. Some results related to the H. Silverman are also the part of our investigation.

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

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.417-430
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• 2013

Let X be a Banach space and ${\psi}$ a continuous convex function on ${\Delta}_{K+1}$ satisfying certain conditions. Let $(X{\bigoplus}X{\bigoplus}{\cdots}{\bigoplus}X)_{\psi}$ be the ${\psi}$-direct sum of X. In this paper, we characterize the K strict convexity, K uniform convexity and uniform non-$l^N_1$-ness of Banach spaces using ${\psi}$-direct sums.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.125-136
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• 2022

For k = 1, 2, let $f_k=h_k+{\bar{g_k}}$ be normalized harmonic right half-plane or vertical strip mappings. We consider the convex combination ${\hat{f}}={\eta}f_1+(1-{\eta})f_2={\eta}h_1+(1-{\eta})h_2+{\overline{\bar{\eta}g_1+(1-\bar{\eta})g_2}}$ and the combination ${\tilde{f}}={\eta}h_1+(1-{\eta})h_2+{\overline{{\eta}g_1+(1-{\eta})g_2}}$. For real 𝜂, the two mappings ${\hat{f}}$ and ${\tilde{f}}$ are the same. We investigate the univalence and directional convexity of ${\hat{f}}$ and ${\tilde{f}}$ for 𝜂 ∈ ℂ. Some sufficient conditions are found for convexity of the combination ${\tilde{f}}$.

• Korean Journal of Mathematics
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• v.31 no.2
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• pp.161-180
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• 2023

In this article, we will utilize (α, m)-convexity to create a new form of Simpson-Newton inequalities in quantum calculus by using q_𝝔1-integral and q_𝝔1-derivative. Newly discovered inequalities can be transformed into quantum Newton and quantum Simpson for generalized convexity. Additionally, this article demonstrates how some recently created inequalities are simply the extensions of some previously existing inequalities. The main findings are generalizations of numerous results that already exist in the literature, and some fundamental inequalities, such as Hölder's and Power mean, have been used to acquire new bounds.