• Kyungpook Mathematical Journal
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• 제57권3호
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• pp.393-400
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• 2017

Very recently, Srivastava et al. [8] introduced an extension of the Pochhammer symbol and used it to define a generalization of the generalized hypergeometric functions. In this paper, by using the generalized Pochhammer symbol, we extend the generalized Hurwitz-Lerch Zeta function by Goyal and Laddha [6] and investigate some interesting properties which include various integral representations, Mellin transforms, differential formula and generating function. Some interesting special cases of our main results are also considered.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권1호
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• pp.11-21
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• 2014

The present paper is concerned with the notions of Lipschitz and asymptotic stability for perturbed nonlinear differential system knowing the corresponding stability of nonlinear differential system. We investigate Lipschitz and asymtotic stability for perturbed nonlinear differential systems. The main tool used is integral inequalities of the Bihari-type, in special some consequences of an extension of Bihari's result to Pinto and Pachpatte, and all that sort of things.

• East Asian mathematical journal
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• 제28권5호
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• pp.553-559
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• 2012

The noncommutative extension of the complex numbers for the four dimensional real space is a quaternion. R. Fueter, C. A. Deavours and A. Subdery have developed a theory of quaternion analysis. M. Naser and K. N$\hat{o}$no have given several results for integral formulas of hyperholomorphic functions in Clifford analysis. We research the properties of hyperholomorphic functions on $\mathbb{C}^2{\times}\mathbb{C}^2$.

• 대한수학회지
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• 제55권1호
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• pp.29-42
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• 2018

We construct bounded linear integral operators that giving solutions to the ${\bar{\partial}}$-equation in $L^p$-spaces and with compact supports on a q-convex intersection ($q{\geq}1$) with ${\mathcal{C}}^3$ boundary in $K{\ddot{a}}hler$ manifolds, and we apply it to obtain a Hartogs-like extension theorems for ${\bar{\partial}}$-closed forms for some bidegree.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.531-542
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• 2002

In this paper we deal with a sequence of positive linear operators ${{R_n}}^{[$\beta$]}$ approximating functions on the unbounded interval [0, $\infty$] which were firstly used by K. balazs and J. Szabados. We give pointwise estimates in the framework of polynomial weighted function spaces. Also we establish a Voronovskaja type theorem in the same weighted spaces for ${{K_n}}^{[$\beta$]}$ operators, representing the integral generalization in Kantorovich sense of the ${{R_n}}^{[$\beta$]}$.

• Korean Journal of Mathematics
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• 제24권3호
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• pp.537-543
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• 2016

Let D be an integral domain, X be an indeterminate over D, D[X] be the polynomial ring over D, and D(X) be the Nagata ring of D. Let [d] be the star operation on D[X], which is an extension of the d-operation on D as in [5, Theorem 2.3]. In this paper, we show that D is a sharp domain if and only if D[X] is a [d]-sharp domain, if and only if D(X) is a sharp domain.

• 대한수학회보
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• 제44권4호
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• pp.743-751
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• 2007

The aim of this article is to derive twenty five transformation formulas in the form of a single result for the triple hypergeometric series $X_8$ introduced earlier by Exton. The results are derived with the help of generalized Watson#s theorem obtained earlier by Lavoie et al. An interesting special cases are also pointed out.

• Kyungpook Mathematical Journal
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• 제54권3호
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• pp.463-469
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• 2014

In this paper, we construct new q-extension of Euler polynomials with weight 0. These modified q-Euler polynomials are useful to study various identities of Carlitz's q-Bernoulli numbers.

• Kyungpook Mathematical Journal
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• 제53권1호
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• pp.25-35
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• 2013

In this paper, we introduce and study the concept of "strongly $t$-linked extensions", which is a stronger version of $t$-linked extensions of integral domains. We show that for an extension of Pr$\ddot{u}$fer $v$-multiplication domains, this concept is equivalent to that of "$w$-faithfully flat".

• Kyungpook Mathematical Journal
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• 제45권4호
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• pp.491-502
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• 2005

The main purpose of this paper is to extend the exponentially convex functions which are defined and exponentially convex on a cylinderical neighborhood in the Heisenberg group. They are expanded in terms of an integral transform associated to the sub-Laplacian operator. Extension of such functions on abelian Lie group are studied in [15].