• Communications of the Korean Mathematical Society
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• 제14권1호
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• pp.217-222
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• 1999

The aim of this research is to provide a generalization of the well-known, interesting and useful identity due to Preece by using classical Dixon`s theorem on a sum of \ulcornerF\ulcorner.

• Honam Mathematical Journal
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• 제38권1호
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• pp.25-37
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• 2016

In 1972, Andrews derived the basic analogue of Gauss's second summation theorem and Bailey's theorem by implementing basic analogue of Kummer's theorem into identity due to Jackson. Recently Lavoie et.al. derived many results closely related to Kummer's theorem, Gauss's second summation theorem and Bailey's theorem and also Rakha et. al. derive the basic analogues of results closely related Kummer's theorem. The aim of this paper is to derive basic analogues of results closely related Gauss's second summation theorem and Bailey's theorem. Some applications and limiting cases are also considered.

• Bulletin of the Korean Mathematical Society
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• 제43권4호
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• pp.861-868
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• 2006

We present a Choquet-Deny-type theorem for downward filtering convex sets of continuous functions and show that the Identity Korovkin cone of a downward filtering convex cone S is exactly the uniform closure of S.

• East Asian mathematical journal
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• 제35권5호
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• pp.529-534
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• 2019

The purpose of this article is to present The $Carath{\acute{e}}odory$-Cartan-Kaup-Wu theorem for connected Kobayashi hyperbolic almost complex manifolds.

• Kyungpook Mathematical Journal
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• 제59권2호
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• pp.293-299
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• 2019

A number of identities associated with the product of generalized hypergeometric series have been investigated. In this paper, we aim to establish an identity involving the product of the generalized hypergeometric series $_2F_2$. We do this using the generalized Kummer-type II transformation due to Rathie and Pogany and another identity due to Bailey. The result presented here, being general, can be reduced to a number of relatively simple identities involving the product of generalized hypergeometric series, some of which are observed to correspond to known ones.

• Communications of the Korean Mathematical Society
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• 제30권2호
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• pp.103-108
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• 2015

Fox [2] presented an interesting identity for $_pF_q$ which is expressed in terms of a finite summation of $_pF_q$'s whose involved numerator and denominator parameters are different from those in the starting one. Moreover Fox [2] found a very interesting and general summation formula for $_3F_2(1/2)$ as a special case of his above-mentioned general identity with the help of Kummer's second summation theorem for $_2F_1(1/2)$. Here, in this paper, we show how two general summation formulas for $$_3F_2\[\array{\hspace{110}{\alpha},{\beta},{\gamma};\\{\alpha}-m,\;\frac{1}{2}({\beta}+{\gamma}+i+1);}\;{\frac{1}{2}}\]$$, m being a nonnegative integer and i any integer, can be easily established by suitably specializing the above-mentioned Fox's general identity with, here, the aid of generalizations of Kummer's second summation theorem for $_2F_1(1/2)$ obtained recently by Rakha and Rathie [7]. Several known results are also seen to be certain special cases of our main identities.

• Bulletin of the Korean Mathematical Society
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• 제50권6호
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• pp.1973-1979
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• 2013

The main purpose of this paper is to give the Wintner theorem in unital complete random normed algebras which is a random generalization of the classical Wintner theorem in Banach algebras. As an application of the Wintner theorem in unital complete random normed algebras, we also obtain that the identity operator on a complete random normed module is not a commutator.

• Honam Mathematical Journal
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• 제21권1호
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• pp.49-56
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• 1999

The object of this note is to provide various methods for proving two results contiguous to Kummer's second theorem by using the classical Gauss's summation theorem and contiguous relations.

• East Asian mathematical journal
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• 제14권1호
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• pp.157-163
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• 1998

The aim of this note is to prove Vandermonde's convolution theorem by using the theory of hypergeometric series as suggested in literature which does not seem to be easy to justify it. We also provide an interesting identity and its application.

• Bulletin of the Korean Mathematical Society
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• 제36권4호
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• pp.655-660
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• 1999

Let R be an integral domain with identity. In this paper we will show that if R is integrally closed or if t-dim $R{\leq}1$, then R[{$X_{\alpha}$}] satisfies the principal ideal theorem for each family {$X_{\alpha}$} of algebraically independent indeterminates if and only if R is an S-domain and it satisfies the principal ideal theorem.