• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.613-621
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• 2017

In this paper, we have constructed subclasses of bi-univalent functions associated with ${\lambda}$-bi-pseudo-starlike functions in the unit disc U. Furthermore we established bound on the coefficients for the subclasses $S^{\lambda}_{\Sigma}(k,{\alpha})$ and $S^{\lambda}_{\Sigma}(k,{\beta})$.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1277-1292
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• 2009

This paper is an attempt to stress the usefulness of the multivariable special functions. In this paper, we derive generating relations involving 3-variable 2-parameter Tricomi functions by using Lie-algebraic techniques. Further we derive certain new and known generating relations involving other forms of Tricomi and Bessel functions as applications.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.181-191
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• 2006

In this paper, multiobjective generalized fractional programming problems with set functions are considered, in which objective functions are maximum of finite fractional set functions. At first, optimality conditions are established. Then, saddle existence theorem is proved.

• Kyungpook Mathematical Journal
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• v.55 no.3
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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.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.781-794
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• 2020

In this article, we investigate the upper bounds on the coefficients for inverse of functions belongs to certain classes of univalent functions and in particular for the functions convex in one direction. Bounds on the Fekete-Szegö functional and third order Hankel determinant for these classes have also investigated.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1213-1235
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• 2016

We prove a uniqueness theorem of nonconstant meromorphic functions sharing three distinct values IM and a fourth value CM with their shifts, and prove a uniqueness theorem of nonconstant entire functions sharing two distinct small functions IM with their shifts, which respectively improve Corollary 3.3(a) and Corollary 2.2(a) from [12], where the meromorphic functions and the entire functions are of hyper order less than 1. An example is provided to show that the above results are the best possible. We also prove two uniqueness theorems of nonconstant meromorphic functions sharing four distinct values with their difference operators.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1239-1248
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• 2018

Recently, many authors have obtained several hypergeometric identities involving hypergeometric functions of one and multi-variables such as the Appell's functions and Horn's functions. In this paper, we obtain several new transformations suitably by applying the fractional calculus operator to these hypergeometric identities, which was introduced recently by Tremblay.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.95-106
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• 2009

A comprehensive class of starlike univalent functions defined by Dziok-Srivastava operator is introduced. Necessary and sufficient coefficient bounds are given for functions in this class to be starlike. Further distortion bounds, extreme points and results on partial sums are investigated.

• East Asian mathematical journal
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• v.33 no.3
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• pp.309-315
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• 2017

In this paper, we investigate the regularities of the hyper-complex valued functions of the split quaternion variables. We define several differential operators for the split qunaternionic function. We research several left split regular functions for each differential operators. We also investigate split harmonic functions. And we find the corresponding Cauchy-Riemann system and the corresponding Cauchy theorem for each regular functions on the split quaternion field.

• Honam Mathematical Journal
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• v.33 no.2
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• pp.129-142
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• 2011

A (presumably) new class of generalized triple hyper-geometric functions is presented. We also give integral representations of Laplace type for certain special cases of the new class of functions.