• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.649-656
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• 2015

In this paper we investigate some symmetric property of the twisted q-Euler zeta functions and twisted q-Euler polynomials.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.647-657
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• 2023

The aim of this paper is to study certain subclass ${\tilde{S^q_{\Sigma}}}({\lambda},\,{\alpha},\,t,\,s,\,p,\,b)$ of analytic and bi-univalent functions which are defined by using symmetric q-derivative operator. We estimate the second and third coefficients of the Taylor-Maclaurin series expansions belonging to the subclass and upper bounds for Feketo-Szegö inequality. Furthermore, some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.165-173
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• 2018

In this paper we obtain the bounds of the third Hankel determinants for the classes $\mathcal{S}^*({\alpha})$ of starlike functions of order ${\alpha}$ and $\mathcal{K}({\alpha}$) of convex functions of order ${\alpha}$. Moreover,we derive the sharp bounds for functions in these classes which are additionally 2-fold or 3-fold symmetric.

• Journal for History of Mathematics
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• v.34 no.2
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• pp.39-54
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• 2021

One of the topics in school mathematics is the relation between the roots and the coefficients of equations. It deals with the way to find the roots out of the coefficients of equations. One of the concepts derived from the theory of equations is symmetric functions. Symmetry is a kind of functionality of human cognition. It is, in mathematics, geometrically related to the congruence and the similarity of figures, and algebraically a kind of invariants. We look at stories on the appearance of symmetric functions through the development of the theory of equations.

• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.997-1006
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• 2024

In this paper, making use of symmetric differential operator, we introduce a new class of ℓ-symmetric - mutually adjoint functions. To make this study more comprehensive and versatile, we have used a differential operator involving three-parameter extension of the well-known Mittag-Leffler functions. Mainly we investigated the inclusion relation and subordination conditions which are the main results of the paper. To establish connections or relations with earlier studies, we have presented applications of main results as corollaries.

• Communications for Statistical Applications and Methods
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• v.14 no.3
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• pp.583-592
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• 2007

Given the moments of a symmetric random variable, its density and distribution functions can be accurately approximated by making use of the algorithm proposed in this paper. This algorithm is specially designed for approximating symmetric distributions and comprises of four phases. This approach is essentially based on the transformation of variable technique and moment-based density approximants expressed in terms of the product of an appropriate initial approximant and a polynomial adjustment. Probabilistic quantities such as percentage points and percentiles can also be accurately determined from approximation of the corresponding distribution functions. This algorithm is not only conceptually simple but also easy to implement. As illustrated by the first two numerical examples, the density functions so obtained are in good agreement with the exact values. Moreover, the proposed approximation algorithm can provide the more accurate quantities than direct approximation as shown in the last example.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1703-1711
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• 2018

The main aim of this paper is to study the fourth Hankel determinant for the class of functions with bounded turning. We also investigate for 2-fold symmetric and 3-fold symmetric functions.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.179-192
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• 1997

An algorithm to get an optimal choice for the number of symmetric quadrature points is given to find symmetric quadrature points is given to find symmetric quadrature for-mulas over a unit disk with a minimal number of points even when a high degree of polynomial precision is required. The symmetric quad-rature formulas for numerical integration over a unit disk of complete polynomial functions up to degree 19 are presented.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.671-679
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• 2018

Abstract of the article can be written hereAbstract of the article can be written here. Recently, several authors have studied the symmetric identities for special functions(see [3,5-11,14,17,18,20-22]). In this paper, we study the symmetric identities of the degenerate modified q-Euler polynomials under the symmetric group.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.589-598
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• 2006

In the present investigation, sharp upper bounds of $|a3-{\mu}a^2_2|$ for functions $f(z)=z+a_2z^2+a_3z^3+...$ belonging to certain subclasses of starlike and convex functions with respect to symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szego inequalities for certain classes of functions defined through fractional derivatives are obtained.