On certain subclasses of multivalent functions with varying arguments of coefficients

Shigeyoshi Owa; Mohamed Kamal Aouf; Hanaa Zayed

doi:10.5269/bspm.43780

Shigeyoshi Owa “1 Decembrie 1918” University of Alba Iulia
Mohamed Kamal Aouf Mansoura University
Hanaa Zayed Menofia University

Resumo

In this paper we introduce and study new classes VM_{p,η}(λ,α,β) and VN_{p,η}(λ,α,β) of multivalent functions with varying arguments of coefficients. We obtain coefficients inequalities, distortion theorems and extreme points for functions in these classes. Also, we investigate several distortion inequalities involving fractional calculus. Finally, results on partial sums are considerd.

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Biografia do Autor

Shigeyoshi Owa, “1 Decembrie 1918” University of Alba Iulia

Honorary Professor

Referências

H. A. Al-Kharsani, Multiplier transformations and k−uniformly p−valent starlike functions, General Math. 17 (2009), no. 1, 13-22.

M. K. Aouf, On fractional derivatives and fractional integrals of certain subclasses of starlike and convex functions, Math. Japon. 35 (1990), no. 5, 831-837.

M. K. Aouf and J. Dziok, Distortion and convolutional theorems for operators of generalized fractional calculus involving Wright function, J. Appl. Anal. 14(2008), no. 2, 183-192. https://doi.org/10.1515/JAA.2008.183

M. K. Aouf, R. M. El-Ashwah, A. A. M. Hassan and A. H. Hassan, Multivalent functions with varying arguments, Int. J. Open Problems Complex Analysis 5(2013), no. 1, 9-17. https://doi.org/10.12816/0005994

M. K. Aouf, A. O. Mostafa and H. M. Zayed, Some characterizations of integral operators associated with certain classes of p-valent functions defined by the Srivastava-Saigo-Owa fractional differintegral operator, Complex Anal. Oper. Theory 10(2016), no. 6, 1267-1275. https://doi.org/10.1007/s11785-015-0508-1

M. K. Aouf, A. O. Mostafa and H. M. Zayed, On certain subclasses of multivalent functions defined by a generalized fractional differintegral operator, Afr. Mat. 28(2017), no. 1-2, 99-107. https://doi.org/10.1007/s13370-016-0433-0

A. O. Mostafa, M. K. Aouf, H. M. Zayed and T. Bulboaca, Multivalent functions associated with Srivastava-Saigo-Owa fractional differintegral operator, Rev. R. Acad. Cienc. Exactas Fıs. Nat. Ser. A Math. 112(2018), 1409-1429. https://doi.org/10.1007/s13398-017-0436-1

S. Owa, On the distortion theorems. I, Kyungpook Math. J. 18 (1978), 53-59.

S. Owa, On certain classes of univalent functions with varying arguments, Simon Stevin 59 (1985), no. 3, 331-347.

S. Owa, On certain classes of p−valent functions with negative coefficients, Simon Stevin 59 (1985), no. 3, 385-402.

H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. Appl. 209 (1997), 221-227. https://doi.org/10.1006/jmaa.1997.5361

H. Silverman, Univalent functions with varying arguments, Houston J. Math. 7 (1981), no. 2, 283-287.

H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51 (1975), 109-116. https://doi.org/10.1090/S0002-9939-1975-0369678-0

E. M. Silvia, On partial sums of convex functions of order α, Houston J. Math. 11 (1985), no. 3, 397-404.

H. M. Srivastava and M. K. Aouf, A certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients. I and II, J. Math. Anal. Appl. 171 (1992), 1-13; ibid. 192 (1995), 973-688. https://doi.org/10.1016/0022-247X(92)90373-L

H. M. Srivastava and M. K. Aouf, Some applications of fractional calculus operators to certain subclasses of prestarlike functions with negative coefficients, Computers Math. Appl. 30 (1995), no. 1, 53-61. https://doi.org/10.1016/0898-1221(95)00067-9

H. M. Srivastava and S. Owa, An application of the fractional derivative, Math. Japon. 29 (1984), 383-389.

H. M. Srivastava and S. Owa (Editors)., Univalent Functions, Fractional Calculus, and Their Applications, Halsted press (Ellis Horwood Limited Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1989.