• Title/Summary/Keyword: Lommel functions

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BOUNDS AND INEQUALITIES OF THE MODIFIED LOMMEL FUNCTIONS

  • Mondal, Saiful R.
    • Communications of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.573-583
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    • 2019
  • This article studies the monotonicity, log-convexity of the modified Lommel functions by using its power series and infinite product representation. Some properties for the ratio of the modified Lommel functions with the Lommel function, sinh and cosh are also discussed. As a consequence, $Tur{\acute{a}}n$ type and reverse $Tur{\acute{a}}n$ type inequalities are given. A Rayleigh type function for the Lommel functions are derived and as an application, we obtain the Redheffer-type inequality.

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 $H^p$.

SUBCLASSES OF ANALYTIC FUNCTIONS DEFINED BY LOMMEL OPERATOR

  • Altinkaya, Sahsene;Badar, Rizwan Salim;Noor, Khalida Inayat
    • Communications of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.567-574
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    • 2022
  • We use convolution techniques to define certain classes of starlike functions which are associated with Lommel operator. Some inclusion results are investigated. It is also shown that these classes are invariant under Bernardi integral operator.

CERTAIN GEOMETRIC PROPERTIES OF MODIFIED LOMMEL FUNCTIONS

  • Din, Muhey U;Yalcin, Sibel
    • Honam Mathematical Journal
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    • v.42 no.4
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    • pp.719-731
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    • 2020
  • In this article, we find some sufficient conditions under which the modified Lommel function is close-to-convex with respect to - log(1 - z) and ${\frac{1}{2}}\;{\log}\;\({\frac{1+z}{1-z}}\)$. Starlikeness, convexity and uniformly close-to-convexity of the modified Lommel function are also discussed. Some results related to the H. Silverman are also the part of our investigation.