• Bulletin of the Korean Mathematical Society
• /
• v.48 no.1
• /
• pp.151-156
• /
• 2011

In this research paper, motivated by the extension of the Euler type I transformation obtained very recently by Rathie and Paris, the authors aim at presenting the extensions of Euler type II transformation. In addition to this, a natural extension of the classical Saalsch$\ddot{u}$tz's summation theorem for the series $_3F_2$ has been investigated. Two interesting applications of the newly obtained extension of classical Saalsch$\ddot{u}$tz's summation theorem are given.

• Journal of the Chungcheong Mathematical Society
• /
• v.3 no.1
• /
• pp.111-113
• /
• 1990

We apply Bredikhin's theorem to the distribution of prime numbers in arithmetic progressions.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.3
• /
• pp.503-511
• /
• 2010

We prove a common fixed point theorem for S-contraction mappings without continuity. Using this result we obtain an approximating curve for S-nonexpansive mappings in a Banach space and prove Browder's type strong convergence theorem for this approximating curve. The demiclosedness principle for S-nonexpansive mappings is also established.

• Korean Journal of Mathematics
• /
• v.12 no.2
• /
• pp.147-154
• /
• 2004

In this paper we give several necessary and sufficient conditions for an operator on the Hilbert space H 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 ${\sigma}(T)$. Furthermore, it is shown that if $T{\in}B(H)$ is a compact operator or a Riesz Operator then T obeys Browder's theorem and Weyl's theorem holds if and only if Browder's holds.

• East Asian mathematical journal
• /
• v.34 no.5
• /
• pp.571-575
• /
• 2018

Let D be an integral domain, ${\ast}$ a star-operation on D, and S a (not necessarily saturated) multiplicative subset of D. In this article, we prove the Cohen type theorem for $S-{\ast}_{\omega}$-principal ideal domains, which states that D is an $S-{\ast}_{\omega}$-principal ideal domain if and only if every nonzero prime ideal of D (disjoint from S) is $S-{\ast}_{\omega}$-principal.

• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.3
• /
• pp.321-326
• /
• 2008

In this note, using the separation theorem for convex sets, we will give a two functions version generalization of Fan's minimax theorem by relaxing the convexlike assumption to the weak convexlike condition.

• Journal of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.285-291
• /
• 1997

In this paper, we obtain an abstract formulation of a fixed point theorem for nonexpansive mappings. Our theorem is a non-metric version of Kirk's original theorem.

• Bulletin of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.491-493
• /
• 1997

This is to clarify that Taskovic's extension of the Brouwer fixed point theorem is incorrectly stated.

• Korean Journal of Mathematics
• /
• v.17 no.1
• /
• pp.37-41
• /
• 2009

We would like to propose Dirichlet-Jordan theorem on the space of summable in measure(SIM). Surely, this is a kind of extension of bounded variation([1, 4]), and considered as an application of fuzzy set such that ${\alpha}$-cut is 0.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.1
• /
• pp.29-35
• /
• 2010

In this note, we will prove a new equilibrium existence theorem for a compact acyclic strategic game by using Begle's fixed point theorem.