• 제목/요약/키워드: Analytic Inequalities

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FEKETE-SZEGÖ INEQUALITIES FOR A NEW GENERAL SUBCLASS OF ANALYTIC FUNCTIONS INVOLVING THE (p, q)-DERIVATIVE OPERATOR

  • Bulut, Serap
    • 대한수학회논문집
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    • 제37권3호
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    • pp.723-734
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    • 2022
  • In this work, we introduce a new subclass of analytic functions of complex order involving the (p, q)-derivative operator defined in the open unit disc. For this class, several Fekete-Szegö type coefficient inequalities are derived. We obtain the results of Srivastava et al. [22] as consequences of the main theorem in this study.

APPLICATIONS OF THE JACK'S LEMMA FOR ANALYTIC FUNCTIONS CONCERNED WITH ROGOSINSKI'S LEMMA

  • Ornek, Bulent Nafi
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제28권3호
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    • pp.235-246
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    • 2021
  • In this study, a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions, is considered.The results of Rogosinskis lemma and Jacks lemma have been utilized to derive novel inequalities. Also, these inequalities have been strengthened by considering the critical points which are different from zero.

ON BOUNDS FOR THE DERIVATIVE OF ANALYTIC FUNCTIONS AT THE BOUNDARY

  • Ornek, Bulent Nafi;Akyel, Tugba
    • Korean Journal of Mathematics
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    • 제29권4호
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    • pp.785-800
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    • 2021
  • In this paper, we obtain a new boundary version of the Schwarz lemma for analytic function. We give sharp upper bounds for |f'(0)| and sharp lower bounds for |f'(c)| with c ∈ ∂D = {z : |z| = 1}. Thus we present some new inequalities for analytic functions. Also, we estimate the modulus of the angular derivative of the function f(z) from below according to the second Taylor coefficients of f about z = 0 and z = z0 ≠ 0. Thanks to these inequalities, we see the relation between |f'(0)| and 𝕽f(0). Similarly, we see the relation between 𝕽f(0) and |f'(c)| for some c ∈ ∂D. The sharpness of these inequalities is also proved.

FEKETE-SZEGÖ INEQUALITIES FOR A SUBCLASS OF ANALYTIC BI-UNIVALENT FUNCTIONS DEFINED BY SĂLĂGEAN OPERATOR

  • BULUT, Serap
    • 호남수학학술지
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    • 제39권4호
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    • pp.591-601
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    • 2017
  • In this paper, by means of the $S{\breve{a}}l{\breve{a}}gean$ operator, we introduce a new subclass $\mathcal{B}^{m,n}_{\Sigma}({\gamma};{\varphi})$ of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$. For functions belonging to this class, we consider Fekete-$Szeg{\ddot{o}}$ inequalities.

Coefficient Inequalities for Certain Subclasses of Analytic Functions Defined by Using a General Derivative Operator

  • Bulut, Serap
    • Kyungpook Mathematical Journal
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    • 제51권3호
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    • pp.241-250
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    • 2011
  • In this paper, we define new classes of analytic functions using a general derivative operator which is a unification of the S$\breve{a}$l$\breve{a}$gean derivative operator, the Owa-Srivastava fractional calculus operator and the Al-Oboudi operator, and discuss some coefficient inequalities for functions belong to this classes.

SOME NEW INTEGRAL MEANS INEQUALITIES AND INCLUSION PROPERTIES FOR A CLASS OF ANALYTIC FUNCTIONS INVOLVING CERTAIN INTEGRAL OPERATORS

  • Raina, R.K.;Bansal, Deepak
    • East Asian mathematical journal
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    • 제24권4호
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    • pp.347-358
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    • 2008
  • In this paper we investigate integral means inequalities for the integral operators $Q_{\lambda}^{\mu}$ and $P_{\lambda}^{\mu}$ applied to suitably normalized analytic functions. Further, we obtain some neighborhood and inclusion properties for a class of functions $G{\alpha}({\phi}, {\psi})$ (defined below). Several corollaries exhibiting the applications of the main results are considered in the concluding section.

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GENERALIZED MINIMAX THEOREMS IN GENERALIZED CONVEX SPACES

  • Kim, Hoon-Joo
    • 호남수학학술지
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    • 제31권4호
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    • pp.559-578
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    • 2009
  • In this work, we obtain intersection theorem, analytic alternative and von Neumann type minimax theorem in G-convex spaces. We also generalize Ky Fan minimax inequality to acyclic versions in G-convex spaces. The result is applied to formulate acyclic versions of other minimax results, a theorem of systems of inequalities and analytic alternative.

SOME REMARKS ON THE SUBORDINATION PRINCIPLE FOR ANALYTIC FUNCTIONS CONCERNED WITH ROGOSINSKI'S LEMMA

  • Akyel, Tugba
    • Korean Journal of Mathematics
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    • 제29권2호
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    • pp.293-304
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    • 2021
  • In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Rogosinski's lemma, Subordination principle and Jack's lemma were used.

SOME RESULTS FOR THE CLASS OF ANALYTIC FUNCTIONS CONCERNED WITH SYMMETRIC POINTS

  • Ayse Nur Arabaci;Bulent Nafi Ornek
    • Korean Journal of Mathematics
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    • 제31권1호
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    • pp.25-33
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    • 2023
  • This paper's objectives are to present the $\mathcal{H}$ class of analytical functions and explore the many characteristics of the functions that belong to this class. Some inequalities regarding the angular derivative have been discovered for the functions in this class. In addition, the symmetry points on the unit disc are used for the obtained inequalities.