• The Pure and Applied Mathematics
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• v.31 no.1
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• pp.33-48
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• 2024

In this study, we would like to state two refined results related to Hermite Hadamard type inequality for convex functions with two distinct techniques. Hence our obtained results would be better than the results already established for the class of convex functions. Applications to trapezoidal rule and special means are also discussed.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.165-173
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• 2018

In this paper we obtain the bounds of the third Hankel determinants for the classes $\mathcal{S}^*({\alpha})$ of starlike functions of order ${\alpha}$ and $\mathcal{K}({\alpha}$) of convex functions of order ${\alpha}$. Moreover,we derive the sharp bounds for functions in these classes which are additionally 2-fold or 3-fold symmetric.

• Kyungpook Mathematical Journal
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• v.58 no.2
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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.

• 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.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.233-245
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• 2017

In the present paper we introduce and investigate an interesting subclass ${\mathcal{K}}^{(k)}_s({\gamma},p) $ of analytic and p-valently close-to-convex functions in the open unit disk ${\mathbb{U}}$. For functions belonging to this class, we derive several properties as the inclusion relationships and distortion theorems. The various results presented here would generalize many known recent results.

• East Asian mathematical journal
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• v.17 no.2
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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.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.259-266
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• 2022

The present investigation is concerned with certain subclasses of alpha-convex functions with fixed point and defined with subordination in the unit disc E = {z :| z |< 1}. The estimates of the first four coefficients for the functions in these classes are obtained. The results due to various authors follow as special cases.

• 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.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.803-813
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• 2006

We define and investigate a subclass of complex valued harmonic convex functions that are univalent and sense preserving in the open unit disk. We obtain coefficient conditions, extreme points, distortion bounds, convolution conditions for the above family of harmonic functions.

• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.709-729
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• 2002

Using the well known Hermite-Hadamard integral inequality for convex functions, some inequalities for the finite Hilbert transform of functions whose first derivatives are convex are established. Some numerical experiments are performed as well.