• Kyungpook Mathematical Journal
• /
• v.49 no.2
• /
• pp.235-243
• /
• 2009

In this paper, we deal with the problem of uniqueness of meromorphic functions that share two small functions with their derivatives, and obtain the following result which improves a result of Yao and Li: Let f(z) be a nonconstant meromorphic function, k > 5 be an integer. If f(z) and g(z) = $a_1(z)f(z)+a_2(z)f^{(k)}(z)$ share the value 0 CM, and share b(z) IM, $\overline{N}_E(r,f=0=F^{(k)})=S(r)$, f${\equiv}$g, where $a_1(z)$, $a_2(z)$ and b(z) are small functions of f(z).

• Bulletin of the Korean Mathematical Society
• /
• v.45 no.4
• /
• pp.729-737
• /
• 2008

In this paper we characterize multi-Jensen functions f : $V^n\;{\rightarrow}\;W$, where n is a positive integer, V, W are commutative groups and V is uniquely divisible by 2. Moreover, under the assumption that f : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$ is Borel measurable, we obtain representation of f (respectively, f, g, h : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$) such that the Jensen difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;f(x)\;-\;f(y)$$ (respectively, the Pexider difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;g(x)\;-\;h(y))$$ takes values in a countable subgroup of $\mathbb{R}$.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1181-1188
• /
• 2010

q-Volkenborn integrals ([8]) and fermionic invariant q-integrals ([12]) are introduced by T. Kim. By using these integrals, Euler q-zeta functions are introduced by T. Kim ([18]). Then, by using the Euler q-zeta functions, S.-H. Rim, S. J. Lee, E. J. Moon, and J. H. Jin ([25]) studied q-Genocchi zeta functions. And also Y. H. Kim, W. Kim, and C. S. Ryoo ([7]) investigated twisted q-zeta functions and their applications. In this paper, we consider the q-analogue of twisted Lerch type Euler zeta functions defined by $${\varsigma}E,q,\varepsilon(s)=[2]q \sum\limits_{n=0}^\infty\frac{(-1)^n\epsilon^nq^{sn}}{[n]_q}$$ where 0 < q < 1, $\mathfrak{R}$(s) > 1, $\varepsilon{\in}T_p$, which are compared with Euler q-zeta functions in the reference ([18]). Furthermore, we give the q-extensions of the above twisted Lerch type Euler zeta functions at negative integers which interpolate twisted q-Euler polynomials.

• International Journal of Computer Science & Network Security
• /
• v.24 no.1
• /
• pp.85-94
• /
• 2024

In this paper, we present the very first time the generalized notion of (α, β, γ, δ) - convex (concave) function in mixed kind, which is the generalization of (α, β) - convex (concave) functions in 1^st and 2^nd kind, (s, r) - convex (concave) functions in mixed kind, s - convex (concave) functions in 1^st and 2^nd kind, p - convex (concave) functions, quasi convex(concave) functions and the class of convex (concave) functions. We would like to state the well-known Ostrowski inequality via SVN-Riemann Integrals for (α, β, γ, δ) - convex (concave) function in mixed kind. Moreover we establish some SVN-Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are (α, β, γ, δ)-convex (concave) functions in mixed kind by using different techniques including Hölder's inequality and power mean inequality. Also, various established results would be captured as special cases with respect to convexity of function.

• Journal of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.787-811
• /
• 1999

Let M be the maximal ideal space of the Banach algebra $H^{\infty}$ of bounded analytic functions on the open unit disc $\triangle$. For a positive singular measure ${\mu}\;on\;{\partial\triangle},\;let\;{L_{+}}^1(\mu)$ be the set of measures v with $0\;{\leq}\;{\nu}\;{\ll}\;{\mu}\;and\;{{\psi}_{\nu}}$ the associated singular inner functions. Let $R(\mu)\;and\;R_0(\mu)$ be the union sets of $\{$\mid$\psiv$\mid$\;<\;1\}\;and\;\{$\mid${\psi}_{\nu}$\mid$\;<\;0\}\;in\;M\;{\setminus}\;{\triangle},\;{\nu}\;\in\;{L_{+}}^1(\mu)$, respectively. It is proved that if $S(\mu)\;=\;{\partial\triangle}$, where $S(\mu)$ is the closed support set of $\mu$, then $R(\mu)\;=\;R0(\mu)\;=\;M{\setminus}({\triangle}\;{\cup}\;M(L^{\infty}(\partial\triangle)))$ is generated by $H^{\infty}\;and\;\overline{\psi_{\nu}},\;{\nu}\;{\in}\;{L_1}^{+}(\mu)$. It is proved that %d{\theta}(S(\mu))\;=\;0$ if and only if there exists as Blaschke product b with zeros $\{Zn\}_n$ such that $R(\mu)\;{\subset}\;{$\mid$b$\mid$\;<\;1}\;and\;S(\mu)$ coincides with the set of cluster points of $\{Zn\}_n$. While, we proved that $\mu$ is a sum of finitely many point measure such that $R(\mu)\;{\subset}\;\{$\mid${\psi}_{\lambda}$\mid$\;<\;1}\;and\;S(\lambda)\;=\;S(\mu)$. Also it is studied conditions on \mu for which $R(\mu)\;=\;R0(\mu)$.

• Journal of Information Technology Services
• /
• v.13 no.3
• /
• pp.111-128
• /
• 2014

President Park Geun-hye Administration has established the Ministry of Science, ICT and Future Planning (MSIP) to build a creative economy using Information and Communication Technology (ICT). July 2, 2013, The National Assembly has legislated the special act on the ICT promotion and convergence so called special ICT Act. This special ICT Act has reduced the legal basis through legislative process and departmental agreement. Therefore many experts worried that since the MSIP's key functions and roles are being reduced, there will be a limit to the MSIP's endeavor for the advancement of science technology and the ICT promotion and convergence. The establishment of the Agency, together with the formation of 'IT Strategy Committee', is considered to be one of the core items of the Special Act on ICT. MSIP originally planned to integrate the ICT R&D functions scattered across many governmental organizations, including Korea Communications Agency (KCA), KEIT and Korea Creative Contents Agency (KOCCA), into the Agency to separate the national ICT R&D from private R&D and streamline the process of 'discovery-selection-evaluation-commercialization'. The analytical results in this study are supposed to the establishment of efficient ICT governance systems as the practical strategies to actively cope with the changes of ICT convergence environment. It is also expected to the revision on the special ICT Act in the ICT budget and governance. Therefore, MSIP should cover research and development (R&D) as well as major ICT promotion functions to a creative economy.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.65 no.5
• /
• pp.753-759
• /
• 2016

Power automation system to operate power distribution systems can be distinguished by distribution SCADA with remote monitoring and control; and distribution automation system with basic functions such as service restoration to the distribution SCADA; and distribution management system which is operated by various applications in order to enhance distribution system operation performance based on the distribution automation system. In the technological change, a technical boundary of information technology (IT) and operation technology (OT) is being blurred by that new concepts such as interoperability. In addtion, IT/OT convergence has been proposed by the improvement of ICT and power system technology. At the viewpoint, advanced distribution management system (ADMS) to have the new concepts and to increase distribution system operation efficiency through global information and functions from the other systems has been proposed. In order to implement the ADMS, IT and OT have to be employed together on the ADMS; and the concept-based IT/OT convergence concept has been presented. Therefore, this paper introduces ADMS and IT/OT convergence and proposes a design of IT/OT convergence based ADMS system design with configurations and functions.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.2
• /
• pp.367-372
• /
• 2009

In this paper, univalence of a certain integral operator and some interesting properties involving the integral operators on the classes of complex order are obtained. Relevant connections of the results, which are presented in this paper, with various other known results are also pointed out.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.631-640
• /
• 2007

The purpose of this article is to deal with the multiple values and uniqueness of meromorphic functions with small functions in the whole complex plane. We obtain a more general theorem which improves and extends strongly the results of R. Nevanlinna, Li-Qiao, Yao, Yi, and Thai-Tan.

• Kyungpook Mathematical Journal
• /
• v.54 no.4
• /
• pp.511-519
• /
• 2014

In this paper, we prove two uniqueness theorem on meromorphic functions sharing one value which generalize a recent result of R. S. Dyavanal [2], and on the other hand, we relax the nature of sharing value from CM to IM.