• Korean Journal of Mathematics
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• 제12권2호
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• pp.107-115
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• 2004

In this paper, the new subclass denoted by $S_p({\alpha},{\beta},{\xi},{\gamma})$ of $p$-valent holomorphic functions has been introduced and investigate the several properties of the class $S_p({\alpha},{\beta},{\xi},{\gamma})$. In particular we have obtained integral representation for mappings in the class $S_p({\alpha},{\beta},{\xi},{\gamma})$) and determined closed convex hulls and their extreme points of the class $S_p({\alpha},{\beta},{\xi},{\gamma})$.

• Kyungpook Mathematical Journal
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• 제52권4호
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• pp.495-511
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• 2012

In this paper, we prove some inequalities in terms of G$\hat{a}$teaux derivatives for convex functions defined on linear spaces and also give improvement of Jensen's inequality. Furthermore, we give applications for norms, mean $f$-deviations and $f$-divergence measures.

• Korean Journal of Mathematics
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• 제24권2호
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• pp.273-296
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• 2016

Some new trace inequalities for convex functions of self-adjoint operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated. Some trace inequalities for matrices are also derived. Examples for the operator power and logarithm are presented as well.

• 대한수학회보
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• 제37권2호
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• pp.291-301
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• 2000

We give sufficient coefficient conditions for a class of meromorphic univalent harmonic functions that are starlike of some order. Furthermore, it is shown that these conditions are also necessary when the coefficients of the analytic part of the function are positive and the coefficients of the co-analytic part of the function are negative. Extreme points, convolution and convex combination conditions for these classes are also determined. Fianlly, comparable results are given for the convex analogue.

• Kyungpook Mathematical Journal
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• 제59권3호
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• pp.481-491
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• 2019

In the present paper, we investigate the upper bounds on third order Hankel determinants for certain class of close-to-convex functions in the unit disk. Furthermore, we obtain estimates of the Zalcman coefficient functional for this class.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.357-374
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• 2019

In this paper, first we obtain some inequalities of Hadamard type for (h - m)-convex functions via Caputo k-fractional derivatives. Secondly, two integral identities including the (n + 1) and (n+ 2) order derivatives of a given function via Caputo k-fractional derivatives have been established. Using these identities estimations of Hadamard type integral inequalities for the Caputo k-fractional derivatives have been proved.

• 대한수학회논문집
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• 제37권2호
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• pp.537-549
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• 2022

In this paper, we consider a convex univalent function f_α,β which maps the open unit disc 𝕌 onto the vertical strip domain Ω_α,β = {w ∈ ℂ : α < ℜ < (w) < β} and introduce new subclasses of both close-to-convex and bi-close-to-convex functions with respect to an odd starlike function associated with Ω_α,β. Also, we investigate the Fekete-Szegö type coefficient bounds for functions belonging to these classes.

• Korean Journal of Mathematics
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• 제30권4호
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• pp.629-642
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• 2022

In a recent paper, Sakar and Güney introduced a new class of bi-close-to-convex functions and determined the estimates for the general Taylor-Maclaurin coefficients of functions therein. The main purpose of this note is to give a generalization of this class. Also we point out the proof by Sakar and Güney is incorrect and present a correct proof.

• 호남수학학술지
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• 제44권1호
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• pp.17-25
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• 2022

The Hermite-Hadamard integral inequality for F_h-convex functions on time scales is established. The applicability of our results ranges from Optimization problems to Calculus of Variations and to Economics. Application to the Calculus of Variations on time scales is discussed.

• 호남수학학술지
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• 제45권2호
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• pp.340-358
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• 2023

This article establishes an equality for the case of twice-differentiable convex functions with respect to the conformable fractional integrals. With the help of this identity, we prove sundry midpoint-type inequalities by twice-differentiable convex functions according to conformable fractional integrals. Several important inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Using the specific selection of our results, we obtain several new and well-known results in the literature.