• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.531-540
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• 2015

If T is an unbounded hyponormal operator on an infinite dimensional complex Hilbert space H with ${\rho}(T){\neq}{\phi}$, then it is shown that T satisfies Weyl's theorem, generalized Weyl's theorem, Browder's theorem and generalized Browder's theorem. The equivalence of generalized Weyl's theorem with generalized Browder's theorem, property (gw) with property (gb) and property (w) with property (b) have also been established. It is also shown that a-Browder's theorem holds for T as well as its adjoint $T^*$.

• East Asian mathematical journal
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• v.17 no.1
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• pp.147-158
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• 2001

The Gauss summation theorem plays a key role in the theory of(generalized) hypergeometric series. The authors study several proofs of the theorem and consider some applications of it.

• Journal of the Korean Statistical Society
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• v.11 no.2
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• pp.88-93
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• 1982

A local limit theorem for large deviations for the i.i.d. random variables was given by Richter (1957), who used the saddle point method of complex variables to prove it. In this paper we give an alternative form of local limit theorem for large deviations for the i.i.d. random variables which is essentially equivalent to that of Richter. We prove the theorem by more direct and heuristic method under a rather simple condition on the moment generating function (m.g.f.). The theorem is proved without assuming that $E(X_i)=0$.

• Honam Mathematical Journal
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• v.16 no.1
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• pp.111-117
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• 1994

In this note we prove a functional central. limit theorem for LPQD sequences, statisfying some moment conditions. No stationarity is required. Our results imply an extension of Birkel's functional central limit theorem for associated processt'S to an LPQD sequence and an improvement of Birkel's functional central limit theorem for LPQD sequences.

• East Asian mathematical journal
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• v.28 no.5
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• pp.543-552
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• 2012

The aim of this paper is to prove a common fixed point theorem in normed linear spaces for discontinuous, occasionally weakly biased mappings without assuming completeness of the space. We give an example to illustrare our theorem. We also give an application of our theorem to best approximation theory. Our theorem improve the results of Gregus [9], Jungck [12], Pathak, Cho and Kang [22], Sharma and Deshpande [26]-[28].

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.491-502
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• 1998

We obtain new fixed point theorems on maps defined on "locally G-convex" subsets of a generalized convex spaces. Our first theorem is a Schauder-Tychonoff type generalization of the Brouwer fixed point theorem for a G-convex space, and the second main result is a fixed point theorem for the Kakutani maps. Our results extend many known generalizations of the Brouwer theorem, and are based on the Knaster-Kuratowski-Mazurkiewicz theorem. From these results, we deduce new results on collectively fixed points, intersection theorems for sets with convex sections and quasi-equilibrium theorems.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.195-204
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• 2016

We prove, in this note, that a Zabavsky ring R is an elementary divisor ring if and only if R is a $B{\acute{e}}zout$ ring. Many known results are thereby generalized to much wider class of rings, e.g. [4, Theorem 14], [7, Theorem 4], [9, Theorem 1.2.14], [11, Theorem 4] and [12, Theorem 7].

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.11-17
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• 2002

In this paper we give several necessary and sufficient conditions for an operator on the Hilbert space to obey Browder's theorem. And it is shown that if S has totally finite ascent and $T{\prec}S$ then $f(T)$ obeys Browder's theorem for every $f{\in}H({\sigma}(T))$, where $H({\sigma}(T))$ denotes the set of all analytic functions on an open neighborhood of ${\sigma}(T)$.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.932-944
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• 1998

In this paper we first prove a new minimum theorem using the upper semicontinuity of minimizing functions, which is comparable to Berge's theorem. Next, as applications, we shall prove the existence of equilibrium in generalized games and the existence theorem of zeros.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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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.