• Kyungpook Mathematical Journal
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• 제49권2호
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• pp.349-353
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• 2009

In this paper we consider some coefficient estimates in the subclass $SL^*$ of strongly starlike functions defined by a certain geometric condition.

• East Asian mathematical journal
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• 제25권1호
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• pp.39-44
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• 2009

The aim of the present investigation is to give some criterion for certain multivalently analytic functions and (or) multivalently meromorphic functions in the corresponding domains.

• Kyungpook Mathematical Journal
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• 제61권3호
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• pp.495-512
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• 2021

We study the value distribution theory of L-functions and completely resolve a question from Yang [10]. This question is related to L-functions sharing three finite values with meromorphic functions. The main result in this paper extends corresponding results from Li [10].

• International Journal of Computer Science & Network Security
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• 제24권1호
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• pp.85-94
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• 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 Information Science Theory and Practice
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• 제8권4호
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• pp.6-19
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• 2020

The objective of this research is to analyze which functions make up web-based as well as mobile social media services and messengers. Services are clustered by their functionality. A total of 640 individual functions were identified, while investigating altogether 44 selected services in their web and mobile versions. Applying content analysis, functions were assigned to the services. The services were ranked by the number of implemented functions, and the functions were ranked by their occurrence in the services. Cluster analysis was applied to classify the services according to their functionality. Facebook and VKontakte were found to be the ones with the most functions; the most frequently implemented functions are support, profile, and account-related. Cluster analysis revealed six classes for mobile and seven classes for web applications. There is a noteworthy difference regarding the functionality scope between web and mobile applications of the same services. An example for this is Mendeley with 38 functions in the mobile and 91 functions in the web version. This is the first empirical attempt at clustering social media services based on their functionality.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
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• pp.285-288
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• 1998

A least-squares identification method is studied that estimates a finite number of coefficients in the series expansion of a transfer function, where the expansion is in terms of recently introduced generalized basis functions, We will expand and generalize the orthogonal functions as basis functions for dynamical system representations. To this end, use is made of balanced realizations as inner transfer functions. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. We show that the Laplace transform of the expansion for some sets$\Psi_{\kappa}(Z)$ is equivalent to a series expansion . Techniques based on this result are presented for obtaining the coefficients $c_{n}$ as those of a series. One of their important properties is that, if chosen properly, they can substantially increase the speed of convergence of the series expansion. This leads to accurate approximate models with only a few coefficients to be estimated. The set of Kautz functions is discussed in detail and, using the power-series equivalence, the truncation error is obtained.

• 대한수학회보
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• 제60권3호
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• pp.575-591
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• 2023

Motivated by several generalizations of the Pochhammer symbol and their associated families of hypergeometric functions and hypergeometric polynomials, by choosing to use a very generalized Pochhammer symbol, we aim to introduce certain extensions of the generalized Lauricella function F⁽ⁿ⁾_A and the Humbert's confluent hypergeometric function Ψ⁽ⁿ⁾ of n variables with, as their respective particular cases, the second Appell hypergeometric function F₂ and the generalized Humbert's confluent hypergeometric functions Ψ₂ and investigate their several properties including, for example, various integral representations, finite summation formulas with an s-fold sum and integral representations involving the Laguerre polynomials, the incomplete gamma functions, and the Bessel and modified Bessel functions. Also, pertinent links between the major identities discussed in this article and different (existing or novel) findings are revealed.

• Kyungpook Mathematical Journal
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• 제53권1호
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• pp.143-148
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• 2013

The theory of generalized Bessel functions is reformulated within the framework of an operational formalism using the multiplier representation of the Lie group $T_3$ as suggested by Miller. This point of view provides more efficient tools which allow the derivation of generating functions of generalized Bessel functions. A few special cases of interest are also discussed.

• East Asian mathematical journal
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• 제21권1호
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• pp.77-103
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• 2005

The theory of multiple Gamma functions was studied in about 1900 and has, recently, been revived in the study of determinants of Laplacians. There is a class of mathematical constants involved naturally in the multiple Gamma functions. Here we summarize those mathematical constants associated with the Gamma and multiple Gamma functions and will show how they are involved, if possible.

• Kyungpook Mathematical Journal
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• 제59권3호
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• pp.493-503
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• 2019

In the present investigation, we define two new subclasses of analytic and m-fold symmetric bi-univalent functions defined by a linear combination in the open unit disk U. Furthermore, for functions in each of the subclasses introduced here, we establish upper bounds for the initial coefficients ${\mid}a_{m+1}{\mid}$ and ${\mid}a_{2m+1}{\mid}$. Also, we indicate certain special cases for our results.