• Title, Summary, Keyword: Analytic Inequalities

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HARDY SPACE OF LOMMEL FUNCTIONS

  • Yagmur, Nihat
    • Bulletin of the Korean Mathematical Society
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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
    • Honam Mathematical Journal
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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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THE GENERALISED INTEGRATION BY PARTS FORMULA FOR APPELL SEQUENCES AND RELATED RESULTS

  • Dargomir, S.S.
    • Communications of the Korean Mathematical Society
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    • v.19 no.1
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    • pp.75-92
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    • 2004
  • A generalised integration by parts formula for sequences of absolutely continuous functions that satisfy the ${\omega}-Appell$ condition and different estimates for the remainder are provided. Applications for particular instances of such sequences are pointed out as well.

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
    • Communications of the Korean Mathematical Society
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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.

ON SUBCLASSES OF FUNCTIONS WITH BOUNDARY AND RADIUS ROTATIONS ASSOCIATED WITH CRESCENT DOMAINS

  • Afis, Saliu;Noor, Khalida Inayat
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.6
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    • pp.1529-1539
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    • 2020
  • The present work is aimed at presenting some characteristic properties of functions that map open unit disk onto a lune in the right half plane. Furthermore, we introduce subclasses of functions with boundary and radius rotations which are related to crescent regions. Some useful results, which include coefficient inequalities and some subordination properties associated with these subclasses are derived. Consequently, related problems concerning these classes are also studied.