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Fekete–Szegö problem for certain subclasses of analytic functions defined by the combination of differential operators

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Abstract

In this paper, we introduce and study some new subclasses of analytic functions defined by the combination of Al-Oboudi and Ruscheweyh differential operators, and obtain coefficient estimates and Fekete–Szegö inequalities for these new subclasses. The results presented in this paper improve the recent work of Kanas and Darwish (Appl Math Lett 23(7), 777–782, 2010).

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References

  1. Abdel-Gawad, H.R., Thomas, D.K.: The Fekete-Szegö problem for strongly close-to-convex functions. Proc. Am. Math. Soc. 114, 345–349 (1992)

    MATH  Google Scholar 

  2. Al-Oboudi, F.M.: On univalent functions defined by a generalized Sãlãgean operator. Int. J. Math. Math. Sci. 27, 1429–1436 (2004)

    Article  Google Scholar 

  3. Chonweerayoot, A., Thomas, D.K., Upakarnitikaset, W.: On the Fekete-Szegö theorem for close-to-convex functions. Publ. Inst. Math. (Beograd) (N.S.) 66, 18–26 (1992)

    MATH  Google Scholar 

  4. Darus, M., Thomas, D.K.: On the Fekete-Szegö theorem for close-to-convex functions. Math. Jpn. 44, 507–511 (1996)

    MATH  Google Scholar 

  5. Darus, M., Thomas, D.K.: On the Fekete-Szegö theorem for close-to-convex functions. Math. Jpn. 47, 125–132 (1998)

    MATH  Google Scholar 

  6. Deniz, E., Orhan, H.: The Fekete-Szegö problem for a generalized subclass of analytic functions. Kyungpook Math. J. 50, 37–47 (2010)

    Article  MathSciNet  Google Scholar 

  7. Deniz, E., Çağlar, M., Orhan, H.: The Fekete-Szegö problem for a class of analytic functions defined by Dziok-Srivastava operator. Kodai Math. J. 35, 439–462 (2012)

    Article  MathSciNet  Google Scholar 

  8. Fekete, M., Szegö, G.: Eine Bemerkung über ungerade schlichte Funktionen. J. Lond. Math. Soc. 8, 85–89 (1933)

    Article  Google Scholar 

  9. Kanas, S., Darwish, H.E.: Fekete-Szegö problem for starlike and convex functions of complex order. Appl. Math. Lett. 23(7), 777–782 (2010)

    Article  MathSciNet  Google Scholar 

  10. Keogh, F.R., Merkes, E.P.: A coefficient inequality for certain classes of analytic functions. Proc. Am. Math. Soc. 20, 8–12 (1969)

    Article  MathSciNet  Google Scholar 

  11. Koepf, W.: On the Fekete-Szegö problem for close-to-convex functions. Proc. Am. Math. Soc. 101, 89–95 (1987)

    MATH  Google Scholar 

  12. London, R.R.: Fekete-Szegö inequalities for close-to-convex functions. Proc. Am. Math. Soc. 117, 947–950 (1993)

    MATH  Google Scholar 

  13. Ma, W., Minda, D.: A unified treatment of some special classes of univalent functions. In: Li, Z., Ren, F., Yang, L., Zhang, S. (eds.) Proceeding of the International Conference on Complex Analysis, pp. 157–169. Int. Press, Boston (1994)

  14. Nasr, M.A., Aouf, M.K.: Starlike function of complex order. J. Nat. Sci. Math. 25, 1–12 (1985)

    MathSciNet  MATH  Google Scholar 

  15. Nasr, M.A., Aouf, M.K.: On convex functions of complex order. Mansoura Sci. Bull. 8, 565–582 (1982)

    Google Scholar 

  16. Orhan, H., Arıkan, H.: \(\left( P, Q\right) -\)Lucas polynomial coefficient inequalities of bi-univalent functions defined by the combination of both operators of Al-Oboudi and Ruscheweyh. Afr. Mat. (2020). https://doi.org/10.1007/s13370-020-00847-5

    Article  Google Scholar 

  17. Orhan, H., Deniz, E., Çağlar, M.: Fekete-Szegö problem for certain subclasses of analytic functions. Demonstr. Math. 45(4), 835–846 (2012)

    MATH  Google Scholar 

  18. Orhan, H., Deniz, E., Răducanu, D.: The Fekete-Szegö problem for subclasses of analytic functions defined by a differential operator related to conic domains. Comput. Math. Appl. 59, 283–295 (2010)

    Article  MathSciNet  Google Scholar 

  19. Orhan, H., Răducanu, D.: Fekete-Szegö problem for strongly starlike functions associated with generalized hypergeometric functions. Math. Comput. Model. 50, 430–438 (2009)

    Article  Google Scholar 

  20. Pfluger, A.: The Fekete-Szegö inequality by a variational method. Ann. Acad. Sci. Fenn. Ser. AI 10, 447–454 (1984)

    MATH  Google Scholar 

  21. Pommerenke, C.: Univalent functions. In: Studia Mathematica Mathematische Lehrbucher, Vandenhoeck and Ruprecht, Göttingen (1975)

  22. Răducanu, D., Orhan, H.: Subclasses of analytic functions defined by a generalized differential operator. Int. J. Math. Anal. 4(1), 1–15 (2010)

    MathSciNet  MATH  Google Scholar 

  23. Ruscheweyh, S.: New criteria for univalent functions. Proc. Am. Math. Soc. 49, 109–115 (1975)

    Article  MathSciNet  Google Scholar 

  24. Sălăgean, G.S.: Subclasses of univalent functions. In: Complex analysis–Proc. 5th Rom.-Finn. Semin., Bucharest 1981, Part 1, Lect. Notes Math. 1013, 362-372 (1983)

  25. Wiatrowski, P.: The coefficients of a certain family of holomorphic functions. Zeszyty Nauk. Uniw. Lodz., Nauki. Mat. Przyrod. Ser. II 39, 75–85 (1971)

    MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to express their deepest appreciation to the reviewers for their valuable suggestions and comments to improve the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Letters, Kafkas University, 36100, Kars, Turkey

    Murat Çağlar

  2. Department of Mathematics, Faculty of Science, Atatürk University, 25240, Erzurum, Turkey

    Halit Orhan

Authors
  1. Murat Çağlar
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  2. Halit Orhan
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Correspondence to Murat Çağlar.

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Dedicated to Prof. Dr. Emin ÖZÇAĞ on the occasion of his 60th birthday.

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Çağlar, M., Orhan, H. Fekete–Szegö problem for certain subclasses of analytic functions defined by the combination of differential operators. Bol. Soc. Mat. Mex. 27, 41 (2021). https://doi.org/10.1007/s40590-021-00349-9

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