• Journal of applied mathematics & informatics
• /
• 제9권2호
• /
• pp.531-542
• /
• 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$]}$.

• 대한수학회보
• /
• 제35권2호
• /
• pp.319-324
• /
• 1998

The equation AX = BX implies $A^*X\;=\;B^X$ when A and B are normal (Fuglede-Putnam theorem). In this paper, the hypotheses on A and B can be relaxed by usin a Hilbert-Schmidt operator X: Let A be p-quasihyponormal and let $B^*$ be invertible p-quasihyponormal such that AX = XB for a Hilbert-Schmidt operator X and $|||A^*|^{1-p}||{\cdot}|||B^{-1}|^{1-p}||\;{\leq}\;1$.Then $A^*X\;=\;XB^*$.

• Journal of applied mathematics & informatics
• /
• 제13권1_2호
• /
• pp.277-286
• /
• 2003

In this paper, the Monger Probabilistic n-metric space is presented, some Hex point theorem for set valued mapping are extended to Monger probabilistic n-metric space.

• 대한수학회보
• /
• 제44권4호
• /
• pp.743-751
• /
• 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.

• East Asian mathematical journal
• /
• 제14권1호
• /
• pp.21-26
• /
• 1998

The Fulgede-Putnam theorem asserts as if A and Bare normal operators and X is an operator such that AX=XB, then A*X=XB*. In this paper, we show that if A is k-quasihyponormal and B* is invertible k-quasihyponormal such that AX=XB for a Hilbert-Schmidt operator X, then A*X=XB*.

• 대한수학회보
• /
• 제56권6호
• /
• pp.1423-1433
• /
• 2019

Here we present the right and left Riemann-Liouville fractional fundamental theorems of fractional calculus without any initial conditions for the first time. Then we establish a Riemann-Liouville fractional Polya type integral inequality with the help of generalised right and left Riemann-Liouville fractional derivatives. The amazing fact here is that we do not need any boundary conditions as the classical Polya integral inequality requires. We extend our Polya inequality to Choquet integral setting.

• Korean Journal of Mathematics
• /
• 제27권3호
• /
• pp.645-655
• /
• 2019

In this article, we show that the nuclear operator defined on Banach space has an extending and lifting operator. Also we give new proofs of the well known facts which were given $Pelcz{\acute{y}}nski$ theorem for complemented subspaces of ${\ell}_1$ and Lewis and Stegall's theorem for complemented subspaces of $L_1({\mu})$.

• 대한수학회보
• /
• 제59권5호
• /
• pp.1191-1213
• /
• 2022

In this paper, we will prove the second main theorem for holomorphic curves intersecting the moving hypersurfaces in subgeneral position with index on an angular domain. Our results are an extension of the previous second main theorems for holomorphic curves with moving targets on an angular domain.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제27권1호
• /
• pp.25-27
• /
• 1988

• Kyungpook Mathematical Journal
• /
• 제63권1호
• /
• pp.11-13
• /
• 2023

We give a new proof for the full form of Hilbert's Nullstellensatz based on on integral extension and Noether's Normalization Lemma.