• Title/Summary/Keyword: Strong differential subordination

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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.

ON A FIRST ORDER STRONG DIFFERENTIAL SUBORDINATION AND APPLICATION TO UNIVALENT FUNCTIONS

  • Aghalary, Rasoul;Arjomandinia, Parviz
    • Communications of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.445-454
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    • 2022
  • Using the concept of the strong differential subordination introduced in [2], we find conditions on the functions θ, 𝜑, G, F such that the first order strong subordination θ(p(z)) + $\frac{G(\xi)}{\xi}$zp'(z)𝜑(p(z)) ≺≺ θ(q(z)) + F(z)q'(z)𝜑(q(z), implies p(z) ≺ q(z), where p(z), q(z) are analytic functions in the open unit disk 𝔻 with p(0) = q(0). Corollaries and examples of the main results are also considered, some of which extend and improve the results obtained in [1].

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.