• Title, Summary, Keyword: Differential subordination

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SOME RESULTS ON CERTAIN CLASS OF ANALYTIC FUNCTIONS BASED ON DIFFERENTIAL SUBORDINATION

  • Prajapat, Jugal Kishore;Agarwal, Ritu
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.1
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    • pp.1-10
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    • 2013
  • In the present paper we derive various useful properties and characteristics for certain class of analytic functions by using the techniques of differential subordination. Some interesting corollaries and applications of the results presented here are also discussed.

SOME SUBORDINATION PROPERTIES OF THE LINEAR OPERATOR

  • PANIGRAHI, TRAILOKYA
    • Journal of the Korean Mathematical Society
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    • v.53 no.1
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    • pp.147-159
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    • 2016
  • In this paper, subordination results of analytic function $f{\in}{\mathcal{A}}_p$ involving linear operator ${\mathcal{K}}^{{\delta},{\lambda}}_{c,p}$ are obtained. By applying the differential subordination method, results are derived under some sufficient subordination conditions. On using some hypergeometric identities, corollaries of the main results are derived. Furthermore, convolution preserving properties for a class of multivalent analytic function associated with the operator ${\mathcal{K}}^{{\delta},{\lambda}}_{c,p}$ are investigated.

Differential Subordination and Superordination Results associated with Srivastava-Attiya Integral Operator

  • Prajapat, Jugal Kishore;Mishra, Ambuj Kumar
    • Kyungpook Mathematical Journal
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    • v.57 no.2
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    • pp.233-244
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    • 2017
  • Differential subordination and superordination results associated with a generalized Hurwitz-Lerch Zeta function in the open unit disk are obtained by investigating appropriate classes of admissible functions. In particular some inequalities for generalized Hurwitz-Lerch Zeta function are obtained.

STRONG DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF NEW GENERALIZED DERIVATIVE OPERATOR

  • OSHAH, ANESSA;DARUS, MASLINA
    • Korean Journal of Mathematics
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    • v.23 no.4
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    • pp.503-519
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    • 2015
  • In this work, certain classes of admissible functions are considered. Some strong dierential subordination and superordination properties of analytic functions associated with new generalized derivative operator $B^{{\mu},q,s}_{{\lambda}_1,{\lambda}_2,{\ell},d}$ are investigated. New strong dierential sandwich-type results associated with the generalized derivative operator are also given.

A SUBMARTINGALE INEQUALITY

  • Kim, Young-Ho;Kim, Byung-Il
    • Communications of the Korean Mathematical Society
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    • v.13 no.1
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    • pp.159-170
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    • 1998
  • In this paper, we extend Burkholder's exponential inequality for a strong subordinate of a nonnegative bounded submartingale.

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STRONG DIFFERENTIAL SUBORDINATION AND APPLICATIONS TO UNIVALENCY CONDITIONS

  • Antonino Jose- A.
    • Journal of the Korean Mathematical Society
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    • v.43 no.2
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    • pp.311-322
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    • 2006
  • For the Briot-Bouquet differential equations of the form given in [1] $${{\mu}(z)+\frac {z{\mu}'(z)}{z\frac {f'(z)}{f(z)}\[\alpha{\mu}(z)+\beta]}=g(z)$$ we can reduce them to $${{\mu}(z)+F(z)\frac {v'(z)}{v(z)}=h(z)$$ where $$v(z)=\alpha{\mu}(z)+\beta,\;h(z)={\alpha}g(z)+\beta\;and\;F(z)=f(z)/f'(z)$$. In this paper we are going to give conditions in order that if u and v satisfy, respectively, the equations (1) $${{\mu}(z)+F(z)\frac {v'(z)}{v(z)}=h(z)$$, $${{\mu}(z)+G(z)\frac {v'(z)}{v(z)}=g(z)$$ with certain conditions on the functions F and G applying the concept of strong subordination $g\;\prec\;\prec\;h$ given in [2] by the author, implies that $v\;\prec\;{\mu},\;where\;\prec$ indicates subordination.

Convolution Properties of Certain Class of Multivalent Meromorphic Functions

  • Vijaywargiya, Pramila
    • Kyungpook Mathematical Journal
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    • v.49 no.4
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    • pp.713-723
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    • 2009
  • The purpose of the present paper is to introduce a new subclass of meromorphic multivalent functions defined by using a linear operator associated with the generalized hypergeometric function. Some properties of this class are established here by using the principle of differential subordination and convolution in geometric function theory.

SUBORDINATION RESULTS FOR CERTAIN CLASSES OF MULTIVALENTLY ANALYTIC FUNCTIONS WITH A CONVOLUTION STRUCTURE

  • Prajapat, J.K.;Raina, R.K.
    • East Asian mathematical journal
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    • v.25 no.2
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    • pp.127-140
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    • 2009
  • In this paper a general class of analytic functions involving a convolution structure is introduced. Among the results investigated are the various results depicting useful properties and characteristics of this function class by employing the techniques of differential subordination. Relevances of the main results with some known results are also mentioned briefly.

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SANDWICH-TYPE THEOREMS FOR A CLASS OF INTEGRAL OPERATORS ASSOCIATED WITH MEROMORPHIC FUNCTIONS

  • Cho, Nak-Eun
    • East Asian mathematical journal
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    • v.28 no.3
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    • pp.321-332
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    • 2012
  • The purpose of the present paper is to investigate some subordination and superordination preserving properties of certain integral operators de ned on the space of meromorphic functions in the puncture open unit disk. The sandwich-type theorems for these integral operators are also presented.

On a Class of Meromorphic Functions Defined by Certain Linear Operators

  • Kumar, Shanmugam Sivaprasad;Taneja, Harish Chander
    • Kyungpook Mathematical Journal
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    • v.49 no.4
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    • pp.631-646
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    • 2009
  • In the present investigation, we introduce new classes of p-valent meromorphic functions defined by Liu-Srivastava linear operator and the multiplier transform and study their properties by using certain first order differential subordination and superordination.