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On Kudriasov Conditions for Univalence of Integral Operators Defined by Generalized Bessel Functions

Author

Listed:
  • Mohsan Raza

    (Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan)

  • Sarfraz Nawaz Malik

    (Department of Mathematics, COMSATS University Islamabad, Wah Campus, Wah Cantt 47040, Pakistan)

  • Qin Xin

    (Faculty of Science and Technology, University of the Faroe Islands, Vestarabryggja 15, FO 100 Torshavn, Faroe Islands, Denmark)

  • Muhey U. Din

    (Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan)

  • Luminiţa-Ioana Cotîrlă

    (Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania)

Abstract

In this article, we studied the necessary conditions for the univalence of integral operators that involve two functions: the generalized Bessel function and a function from the well-known class of normalized analytic functions in the open unit disk. The main tools for our discussions were the Kudriasov conditions for the univalency of functions, as well as functional inequalities for the generalized Bessel functions. We included the conditions for the univalency of integral operators that involve Bessel, modified Bessel and spherical Bessel functions as special cases. Furthermore, we provided sufficient conditions for the integral operators that involve trigonometric, as well as hyperbolic, functions as an application of our results.

Suggested Citation

  • Mohsan Raza & Sarfraz Nawaz Malik & Qin Xin & Muhey U. Din & Luminiţa-Ioana Cotîrlă, 2022. "On Kudriasov Conditions for Univalence of Integral Operators Defined by Generalized Bessel Functions," Mathematics, MDPI, vol. 10(9), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1361-:d:796998
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    References listed on IDEAS

    as
    1. Selinger, V., 1995. "Geometric properties of normalized Bessel functions," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 6(2-3), pages 273-277.
    2. Virgil Pescar & Nicoleta Breaz, 2013. "Kudriasov Type Univalence Criteria for Some Integral Operators," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-4, December.
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