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Differential Subordinations for Analytic Functions

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Abstract

In this article, we determine the conditions on \(\beta\) such that \(1+\beta zp^{\prime }(z)\prec \sqrt{1+cz}\) implies \(p(z)\prec (1+Az)/(1+Bz)\) with \(-1\le B<A\le 1\) and \(c\in ( 0,1]\). Similarly some results are also obtained for the expressions \(1+\beta zp^{\prime }(z)/p(z),\ p\left( z\right) +\beta zp^{\prime }(z)/p(z)\) and \(p\left( z\right) +\beta zp^{\prime 2}(z)\). Using these results, we find sufficient conditions for function to be in some subclasses of analytic functions. We also give some applications of these results in the geometric function theory.

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Authors and Affiliations

  1. Department of Mathematics, Government College University, Faisalabad, Pakistan

    Mohsan Raza & Saima Mushtaq

  2. Department of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959, Rzeszów, Poland

    Janusz Sokół

Authors
  1. Mohsan Raza
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  2. Janusz Sokół
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  3. Saima Mushtaq
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Correspondence to Mohsan Raza.

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Raza, M., Sokół, J. & Mushtaq, S. Differential Subordinations for Analytic Functions. Iran J Sci Technol Trans Sci 43, 883–890 (2019). https://doi.org/10.1007/s40995-017-0430-7

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  • DOI: https://doi.org/10.1007/s40995-017-0430-7

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