We establish coefficient bounds for functions from the subclasses of p-valent starlike and p-valent convex functions defined by higher-order derivatives and complex order introduced with the help of a certain nonhomogeneous Cauchy–Euler differential equation with higher-order derivatives. Relevant connections of some of our results with the results obtained earlier are provided.
Similar content being viewed by others
References
O. Altintas, H. Irmak, S. Owa, and H. M. Srivastava, “Coefficient bounds for some families of starlike and convex functions of complex order,” Appl. Math. Lett., 20, No. 12, 1218–1222 (2007).
M. K. Aouf, “p-Valent classes related to convex functions of complex order,” Rocky Mountain J. Math., 15, No. 4, 853–863 (1985).
M. K. Aouf, “On a class of p-valent starlike functions of order α,” Int. J. Math. Math. Sci., 10, No. 4, 733–744 (1987).
M. K. Aouf, “On coefficient bounds of a certain class of p-valent λ-spiral functions of order α,” Int. J. Math. Math. Sci., 10, No. 2, 259–266 (1987).
M. K. Aouf, “A generalization of multivalent functions with negative coefficients,” J. Korean Math. Soc., 25, No. 1, 53–66 (1988).
M. K. Aouf, H. M. Hossen, and H. M. Srivastava, “Some families of multivalent functions,” Comput. Math. Appl., 39, No. 7-8, 39–48 (2000).
M. K. Aouf, “Some families of p-valent functions with negative coefficients,” Acta Math. Univ. Comenian. (N.S.), 78, No. 1, 121–135 (2009).
M. K. Aouf, “On certain multivalent functions with negative coefficients defined by using a differential operator,” Mat. Vesnik, 62, No. 1, 23–35 (2010).
M. K. Aouf, “Bounded p-valent Robertson functions defined by using a differential operator,” J. Franklin Inst., 347, No. 10, 1927–1941 (2010).
M. K. Aouf, H. E. Darwish, and A. E. Alhosseny, “A generalization of p-valent classes related to convex functions,” Demonstr. Math., 33, No. 3, 467–479 (2000).
S. Bulut, “The generalization of the generalized Al-Oboudi differential operator,” Appl. Math. Comput., 215, No. 4, 1448–1455 (2009).
Q. Deng, “Certain subclass of analytic functions with complex order,” Appl. Math. Comput., 208, No. 2, 359–362 (2009).
L. Dileep and S. Latha, “On p-valent functions of complex order,” Demonstr. Math., 45, No. 3, 541–547 (2012).
R. M. El-Ashwah, M. K. Aouf, and S. M. El-Deeb, “Inclusion and neighborhood properties of certain subclasses of p-valent functions of complex order defined by convolution,” Ann. Univ. Mariae Curie-Skłodowska, Sec. A, 65, No. 1, 33–48 (2011).
M. A. Nasr and M. K. Aouf, “On convex functions of complex order,” Bull. Fac. Sci. Mansoura Univ., 9, 565–582 (1982).
M. A. Nasr and M. K. Aouf, “Bounded starlike functions of complex order,” Proc. Indian Acad. Sci. Math. Sci., 92, No. 2, 97–102 (1983).
M. A. Nasr and M. K. Aouf, “Starlike function of complex order,” J. Natur. Sci. Math., 25, No. 1, 1–12 (1985).
S. Owa, “On certain classes of p-valent functions with negative coefficients,” Bull. Belg. Math. Soc. Simon Stevin, 59, 385–402 (1985).
D. A. Patil and N. K. Thakare, “On coefficient bounds of p-valent λ-spiral functions of order α,” Indian J. Pure Appl. Math., 10, No. 7, 842–853 (1979).
Ch. Pommerenke, “On univalent functions, Bloch functions and VMOA,” Math. Ann., 26, No. 3, 199–208 (1978).
M. S. Robertson, “On the theory of univalent functions,” Ann. Math. (2), 37, 374–408 (1936).
H. M. Srivastava, O. Altintas, and S. K. Serenbay, “Coefficient bounds for certain subclasses of starlike functions of complex order,” Appl. Math. Lett., 24, No. 8, 1359–1363 (2011).
H. M. Srivastava, M. K. Aouf, and S. Owa, “Certain classes of multivalent functions of order α and type β,” Bull. Soc. Math. Belg. Sér. B., 42, No. 1, 31–66 (1990).
H. M. Srivastava and S. Owa (editors), Univalent Functions, Fractional Calculus, and Their Applications, Halsted Press (Ellis Harwood Limited, Chichester), John Wiley and Sons, New York (1989).
H. M. Srivastava and S. Owa (editors), Current Topics in Analytic Function Theory, World Scientific, River Edge, NJ (1992).
H. M. Srivastava, S. Owa, and S. K. Chatterjea, “A note on certain classes of starlike functions,” Rend. Semin. Mat. Univ. Padova, 77, 115–124 (1987).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 10, pp. 1308–1316, October, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i10.6258.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Aouf, M.K., Mostafa, A.O. & Bulboacă, T. Coefficient Bounds for Multivalent Classes of Starlike and Convex Functions Defined by Higher-Order Derivatives and Complex Order. Ukr Math J 74, 1490–1499 (2023). https://doi.org/10.1007/s11253-023-02150-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-023-02150-5