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A class of \(\vartheta \)-bi-pseudo-starlike functions with respect to symmetric points associated with Telephone numbers

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Abstract

In this paper we introduce a new class of \(\vartheta \)-bi-pseudo-starlike functions with respect to symmetric points associated with telephone numbers and determine the bounds of the initial Taylor–Maclaurin coefficients and the Fekete–Szegö problem for functions belonging to this class. Some special cases of main results presented here are stated which are new and give better improvement to the initial Taylor-Maclaurin coefficients.

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References

  1. Duren, P.L.: Univalent Functions, In: Grundlehren der Mathematischen Wissenschaften, Band 259, New York, Berlin, Heidelberg and Tokyo, Springer-Verlag, (1983)

  2. Miller, S.S., Mocanu, P.T.: Differential Subordinations Theory and Applications, Series of Monographs and Text Books in Pure and Applied Mathematics, 225, Marcel Dekker, New York, (2000)

  3. Babalola, K.O.: On \(\lambda \)-pseudo-starlike functions. J. Class. Anal. 3(2), 137–147 (2013)

    Article  MathSciNet  Google Scholar 

  4. Sakaguchi, K., Sakaguchi, K.: On a certain univalent map**. J. Math. Soc. Japan 11, 72–75 (1959)

    Article  MathSciNet  Google Scholar 

  5. Wang, G., Gao, C.Y., Yuan, S.M.: On certain subclasses of close-to-convex and quasi-convex functions with respectto \(k-\)symmetric points. J. Math. Anal. Appl. 32(1), 97–106 (2006)

    Article  Google Scholar 

  6. Srivastava, H.M., Mishra, A.K., Gochhayat, P.: Certain subclasses of analytic and bi-univalent functions. Appl. Math. Lett. 23(10), 1188–1192 (2010)

    Article  MathSciNet  Google Scholar 

  7. Brannan, D.A., Clunie, J., Kirwan, W.E.: Coefficient estimates for a class of star-like functions. Canad. J. Math. 22, 476–485 (1970)

    Article  MathSciNet  Google Scholar 

  8. Brannan, D.A., Taha, T.S.: On some classes of bi-univalent functions. Studia Univ. Babes-Bolyai Math. 31(2), 70–77 (1986)

    MathSciNet  Google Scholar 

  9. Lewin, M.: On a coefficient problem for bi-univalent functions. Proc. Amer. Math. Soc. 18, 63–68 (1967)

    Article  MathSciNet  Google Scholar 

  10. Murugusundaramoorthy, G., Sokół, J.: On \(\lambda -\) pseudo bi-starlike functions related to some conic domains. Bull Transilv. Univ. Bras. III: Math. Inform. Phys 12(61), 381–392 (2019)

    MathSciNet  Google Scholar 

  11. Xu, Q.-H., Gui, Y.-C., Srivastava, H.M.: Estimates for a certain subclass of analytic and bi-univalent functions. Appl. Math. Lett. 25, 990–994 (2012)

    Article  MathSciNet  Google Scholar 

  12. Li, X.-F., Wang, A.-P.: Two new subclasses of bi-univalent functions. Inter. Math. Forum 7(30), 1495–1504 (2012)

    MathSciNet  Google Scholar 

  13. Chowla, S., Herstein, I.N., Moore, W.K.: On recursions connected with symmetric groups I. Can. J. Math. 3, 328–334 (1951)

    Article  MathSciNet  Google Scholar 

  14. Knuth, D.E.: The Art of Computer Programming, vol. 3. Addison-Wesley, Boston (1973)

    Google Scholar 

  15. Beissinger, J.S.: Similar constructions for Young tableaux and involutions, and their applications to shiftable tableaux. Discrete Math. 67, 149–163 (1987)

    Article  MathSciNet  Google Scholar 

  16. Riordan, J.: Introduction to Combinatorial Analysis. Dover, Mineola (2002)

    Google Scholar 

  17. Włoch, A., Wołowiec-Musiał, M.: On generalized telephone number, their interpretations and matrix generators. Util. Math. 10, 531–39 (2017)

    MathSciNet  Google Scholar 

  18. Bednarz, U., Wolowiec-Musial, M.: On a new generalization of telephone numbers. Turk. J. Math. 43, 1595–1603 (2019)

    Article  MathSciNet  Google Scholar 

  19. Deniz, E.: Sharp coefficient bounds for starlike functions associated with generalized telephone numbers. Bull. Malays. Math. Sci. Soc. 44, 1525–1542 (2021)

    Article  MathSciNet  Google Scholar 

  20. Murugusundaramoorthy, G., Vijaya, K.: Certain subclasses of snalytic functions associated with generalized telephone numbers, Symmetry 14, Article ID: 1053, (2022)

  21. Vijaya, K., Murugusundaramoorthy, G.: Bi-Starlike functionof complex order involving Mathieu-type series associated with telephone numbers, Symmetry 15, Article ID: 638, (2023)

  22. Pommerenke, Ch.: Univalent Functions, Math. Math, Lehrbucher, Vandenhoeck and Ruprecht, Göttingen, (1975)

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

    Article  MathSciNet  Google Scholar 

  24. Zaprawa, P.: On the Fekete-Szegö problem for classes of bi-univalent functions. Bull. Belg. Math. Soc. Simon Stevin 21(1), 169–178 (2014)

    Article  MathSciNet  Google Scholar 

  25. Mustafa, N., Mrugusundaramoorthy, G., Janani, T.: Second Hankel determinant for a certain subclass of bi-univalent functions. Mediterr. J. Math. 15(3), 119 (2018)

    Article  MathSciNet  Google Scholar 

  26. Srivastava, H.M., Murugusundaramoorthy, G., Bulboacă, T.: The second Hankel determinant for subclasses of Bi-univalent functions associated with a nephroid domain. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 116(4), 145 (2022)

    Article  MathSciNet  Google Scholar 

  27. Priya, H., Sruthakeerthi, B.: Texture analysis using Horadam polynomial coefficient estimate for the class of Sakaguchi kind function. Sci. Rep. 13, 14436 (2023). https://doi.org/10.1038/s41598-023-41734-w

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

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Acknowledgements

We record our sincere thanks to the referees for their valuable suggestions.

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Authors and Affiliations

  1. School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, India

    G. Murugusundaramoorthy & K. Vijaya

  2. Department of Applied Mathematics, Pukyong National University, Busan, 608-737, Korea

    N. E. Cho

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  1. G. Murugusundaramoorthy
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  2. N. E. Cho
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  3. K. Vijaya
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Correspondence to G. Murugusundaramoorthy.

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Murugusundaramoorthy, G., Cho, N.E. & Vijaya, K. A class of \(\vartheta \)-bi-pseudo-starlike functions with respect to symmetric points associated with Telephone numbers. Afr. Mat. 35, 17 (2024). https://doi.org/10.1007/s13370-023-01159-0

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