• 제목/요약/키워드: Analytic Inequalities

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ON THE ANALYTIC PART OF HARMONIC UNIVALENT FUNCTIONS

  • FRASIN BASEM AREF
    • 대한수학회보
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    • v.42 no.3
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    • pp.563-569
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    • 2005
  • In [2], Jahangiri studied the harmonic starlike functions of order $\alpha$, and he defined the class T$_{H}$($\alpha$) consisting of functions J = h + $\bar{g}$ where hand g are the analytic and the co-analytic part of the function f, respectively. In this paper, we introduce the class T$_{H}$($\alpha$, $\beta$) of analytic functions and prove various coefficient inequalities, growth and distortion theorems, radius of convexity for the function h, if the function J belongs to the classes T$_{H}$($\alpha$) and T$_{H}$($\alpha$, $\beta$).

HARDY SPACE OF LOMMEL FUNCTIONS

  • Yagmur, Nihat
    • 대한수학회보
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    • v.52 no.3
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    • pp.1035-1046
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    • 2015
  • In this work we present some geometric properties (like star-likeness and convexity of order ${\alpha}$ and also close-to-convexity of order ($1+{\alpha}$)/2) for normalized of Lommel functions of the first kind. In order to prove our main results, we use the technique of differential subordinations and some inequalities. Furthermore, we present some applications of convexity involving Lommel functions associated with the Hardy space of analytic functions, i.e., we obtain conditions for the function $h_{{\mu},{\upsilon}}(z)$ to belong to the Hardy space $H^p$.

THE FEKETE-SZEGÖ COEFFICIENT INEQUALITY FOR A NEW CLASS OF m-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS SATISFYING SUBORDINATION CONDITION

  • Akgul, Arzu
    • 호남수학학술지
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    • v.40 no.4
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    • pp.733-748
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    • 2018
  • In this paper, we investigate a new subclass $S^{{\varphi},{\lambda}}_{{\Sigma}_m}$ of ${\Sigma}_m$ consisting of analytic and m-fold symmetric bi-univalent functions satisfying subordination in the open unit disk U. We consider the Fekete-$Szeg{\ddot{o}}$ inequalities for this class. Also, we establish estimates for the coefficients for this subclass and several related classes are also considered and connections to earlier known results are made.

ON CERTAIN INTEGRALS OF ANALYTIC FUNCTION

  • Kwon, Oh-Sang;Cho, Na-Keun;Owa, Shigeyoshi
    • East Asian mathematical journal
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    • v.4
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    • pp.33-39
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    • 1988
  • The object of the present paper is to derive some inequalities for certain integrals of functions belonging to the classes A(n), S*(n,$\alpha$) and K(n,$\alpha$). As the special class of our theorems, we have the corresponding result shown by M. $Obradovi\'{c}$ [2].

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ON CERTAIN CLASS OF ANALYTIC FUNCTIONS DEFINED BY CONVOLUTIONS

  • Kwon, Oh-Sang;Cho, Nak-Eun
    • East Asian mathematical journal
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    • v.5 no.1
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    • pp.57-67
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    • 1989
  • We introduce a class $L_{\sigma}*({\alpha},{\beta},{\gamma})$ of functions defined by $f*S_{\sigma}(z)$ of f(z) and $S_{\sigma}(z)=z/(1-z)^{2(1-{\sigma})}$. The present paper is to determine extreme point, coefficient inequalities., distortion Theorem and radius of starlikeness and convexity for functions in $L_{\sigma}*({\alpha},{\beta},{\gamma})$. And we give fractional calculus.

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The Fekete-Szegö Problem for a Generalized Subclass of Analytic Functions

  • Deniz, Erhan;Orhan, Halit
    • Kyungpook Mathematical Journal
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    • v.50 no.1
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    • pp.37-47
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    • 2010
  • In this present work, the authors obtain Fekete-Szeg$\ddot{o}$ inequality for certain normalized analytic function f(z) defined on the open unit disk for which $\frac{(1-{\alpha})z(D^m_{{\lambda},{\mu}}f(z))'+{\alpha}z(D^{m+1}_{{\lambda},{\mu}}f(z))'}{(1-{\alpha})D^m_{{\lambda},{\mu}}f(z)+{\alpha}D^{m+1}_{{\lambda},{\mu}}f(z)}$ ${\alpha}{\geq}0$) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by Hadamard product (or convolution) are given. As a special case of this result, Fekete-Szeg$\ddot{o}$ inequality for a class of functions defined through fractional derivatives is obtained. The motivation of this paper is to generalize the Fekete-Szeg$\ddot{o}$ inequalities obtained by Srivastava et al., Orhan et al. and Shanmugam et al., by making use of the generalized differential operator $D^m_{{\lambda},{\mu}}$.

SOME APPLICATIONS AND PROPERTIES OF GENERALIZED FRACTIONAL CALCULUS OPERATORS TO A SUBCLASS OF ANALYTIC AND MULTIVALENT FUNCTIONS

  • Lee, S.K.;Khairnar, S.M.;More, Meena
    • Korean Journal of Mathematics
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    • v.17 no.2
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    • pp.127-145
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    • 2009
  • In this paper we introduce a new subclass $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ of analytic and multivalent functions with negative coefficients using fractional calculus operators. Connections to the well known and some new subclasses are discussed. A necessary and sufficient condition for a function to be in $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ is obtained. Several distortion inequalities involving fractional integral and fractional derivative operators are also presented. We also give results for radius of starlikeness, convexity and close-to-convexity and inclusion property for functions in the subclass. Modified Hadamard product, application of class preserving integral operator and other interesting properties are also discussed.

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A CERTAIN SUBCLASS OF JANOWSKI TYPE FUNCTIONS ASSOCIATED WITH κ-SYMMETRIC POINTS

  • Kwon, Ohsang;Sim, Youngjae
    • 대한수학회논문집
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    • v.28 no.1
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    • pp.143-154
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    • 2013
  • We introduce a subclass $S_s^{({\kappa})}$(A,B) (-1 ${\leq}$ B < A ${\leq}$ 1) of functions which are analytic in the open unit disk and close-to-convex with respect to ${\kappa}$-symmetric points. We give some coefficient inequalities, integral representations and invariance properties of functions belonging to this class.