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Successive coefficients of functions in classes defined by subordination

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Abstract

The aim of the present paper is to determine bounds on the difference of the moduli of successive coefficients, that is \(\big ||a_{n+1}|-|a_{n}|\big |\) for classes defined by subordination like classes of starlike functions \(\mathcal {S}^*(\varphi )\), and convex functions \(\mathcal {C}(\varphi )\). For various special functions \(\varphi \) corresponding consequences of the main result are also presented that incorporate some known results as the special cases.

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Acknowledgements

The authors would like to thank both reviewer and editor for their helpful advice and suggestions. The fourth author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2019R1I1A3A01050861).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran

    Davood Alimohammadi

  2. Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 316-36155, Shahrood, Iran

    Ebrahim Analouei Adegani

  3. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084, Cluj-Napoca, Romania

    Teodor Bulboacă

  4. Department of Applied Mathematics, College of Natural Sciences, Pukyong National University, Busan, 608-737, Republic of Korea

    Nak Eun Cho

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  1. Davood Alimohammadi
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  2. Ebrahim Analouei Adegani
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  3. Teodor Bulboacă
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  4. Nak Eun Cho
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All authors jointly worked on the results and they read and approved the final manuscript.

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Correspondence to Davood Alimohammadi.

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Dedicated to the memory of the second author’s parents Abbas Analouei Adegani (1936–2009) and Pari Jafari (1944–2009)

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Alimohammadi, D., Analouei Adegani, E., Bulboacă, T. et al. Successive coefficients of functions in classes defined by subordination. Anal.Math.Phys. 11, 151 (2021). https://doi.org/10.1007/s13324-021-00586-1

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  • DOI: https://doi.org/10.1007/s13324-021-00586-1

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