• Korean Journal of Mathematics
• /
• v.25 no.2
• /
• pp.247-259
• /
• 2017

By the use of inequalities for nonnegative Hermitian forms some new inequalities for numerical radius of bounded linear operators in complex Hilbert spaces are established.

• Communications of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.533-547
• /
• 2016

In this paper, a generalized boundary version of $Carath{\acute{e}}odory^{\prime}s$ inequality for holomorphic function satisfying $f(z)= f(0)+a_pz^p+{\cdots}$, and ${\Re}f(z){\leq}A$ for ${\mid}z{\mid}$<1 is investigated. Also, we obtain sharp lower bounds on the angular derivative $f^{\prime}(c)$ at the point c with ${\Re}f(c)=A$. The sharpness of these estimates is also proved.

• Communications of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.1205-1215
• /
• 2018

In this paper, a boundary version of the $Carath{\acute{e}}odory^{\prime}s$ inequality is investigated. We shall give an estimate below ${\mid}f^{\prime}(b){\mid}$ according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and $z_1{\neq}0$. The sharpness of these estimates is also proved.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.6 no.1
• /
• pp.67-80
• /
• 2002

We formulate a pair of nondifferentiable symmetric dual variational problems with a square root term. Under invexity assumptions, we establish weak, strong, converse and self duality theorems for our variational problems by using the generalized Schwarz inequality. Also, we give the static case of our nondifferentiable symmetric duality results.

• Communications of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.201-215
• /
• 2020

In this paper, a boundary version of Carathéodory's inequality on the right half plane for p-valent is investigated. Let Z(s) = 1+c_p (s - 1)^p +c_p+1 (s - 1)^p+1 +⋯ be an analytic function in the right half plane with ℜZ(s) ≤ A (A > 1) for ℜs ≥ 0. We derive inequalities for the modulus of Z(s) function, |Z'(0)|, by assuming the Z(s) function is also analytic at the boundary point s = 0 on the imaginary axis and finally, the sharpness of these inequalities is proved.

• Korean Journal of Mathematics
• /
• v.26 no.2
• /
• pp.191-214
• /
• 2018

The aim of this paper is to investigate the Fekete $Szeg{\ddot{o}}$ inequality for subclass of analytic functions defined by convolution between generalized Al-Oboudi differential operator and Srivastava-Attiya integral operator. Further, application to fractional derivatives are also given.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.1
• /
• pp.189-198
• /
• 2004

In this study we consider quantum dynamical semi-group with a normal faithful invariant state. A quantum dynamical semigroup $\alpha\;=\;\{{\alpha}_t\}_{t{\geq}0}$ is a class of linear normal identity-preserving mappings on a von Neumann algebra M with semigroup property and some positivity condition. We investigate the asymptotic behaviors of the semigroup such as ergodicity or mixing properties in terms of their eigenvalues under the assumption that the semigroup satisfies positivity. This extends the result of [13] which is obtained under the assumption that the semi group satisfy 2-positivity.

• Communications of the Korean Mathematical Society
• /
• v.24 no.1
• /
• pp.99-109
• /
• 2009

The aim of this paper is to find the set of the fixed elements and the set of elements for which equality holds in Schwarz inequality for the KMS-symmetric Markovian semigroup $\{S_t\}_{t{\geq}0}$ given in [10]. As an application, we study some properties such as the ergodicity and the asymptotic behavior of the semigroup.

• Kyungpook Mathematical Journal
• /
• v.54 no.4
• /
• pp.531-543
• /
• 2014

The object of the present paper is to discuss some interesting properties of analytic functions f(z) associated with the subclasses $\mathcal{D}({\beta}_1,{\beta}_2,{\beta}_3;{\lambda})$, $\mathcal{G}({\theta},{\alpha})$ and $\mathcal{Q}({\theta},{\alpha})$. Also, radius problems of $\frac{1}{\delta}f({\delta}z)$ for f(z) in the class $\mathcal{D}({\beta}_1,{\beta}_2,{\beta}_3;{\lambda})$, $\mathcal{G}({\theta},{\alpha})$ and $\mathcal{Q}({\theta},{\alpha})$ are considered.

• Journal of the Korean Mathematical Society
• /
• v.58 no.3
• /
• pp.791-797
• /
• 2021

In this corrigendum, we offer a correction to [J. Korean Math. Soc. 54 (2017), No. 2, 461-477]. We construct a counterexample for the strengthened Cauchy-Schwarz inequality used in the original paper. In addition, we provide a new proof for Lemma 5 of the original paper, an estimate for the extremal eigenvalues of the standard unpreconditioned FETI-DP dual operator.