Certain Class of Bi-Bazilevic Functions with Bounded Boundary Rotation Involving Salăgeăn Operator

Yıl 2020, Cilt: 3 Sayı: 4, 139 - 149, 01.12.2020

Mohamed Kamal Aouf , Tamer Seoudy

https://doi.org/10.33205/cma.781936

Cited By: 6

Öz

In the present paper, we consider certain classes of bi-univalent Bazilevic functions with bounded boundary rotation involving Salăgeăn linear operator to obtain the estimates of their second and third coefficients. Further, certain special cases are also indicated. Some interesting remarks about the results presented here are also discussed.
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Anahtar Kelimeler

Analytic function, Bi-univalent, Bazilevic functions, Sălăgean operator

Kaynakça

• R. M. Ali, S. K. Lee, V. Ravichandran and S. Supramaniam, Coefficient estimates for bi-univalent Ma-Minda stalike and convex functions, Appl. Math. Lett., 25(2012), no. 3, 344--351.
• F. M. Al-Oboudi and M. M. Haidan, Spirallike function of complex order, J. Natural Geometry, 19(2000), 53-72.
• M. K. Aouf, A generalized of functions with real part bounded in the mean on the unit disc, Math. Japon., 33(1988), no. 2, 175-182.
• M. K. Aouf and H. M. Srivastava, Some families of starlike functions with negative coefficients, J. Math. Anal. Appl., 203(1996), no. 3, 762-790.
• M. K. Aouf, T. M. Seoudy: Fekete-Szegö Problem for Certain Subclass of Analytic Functions with Complex Order Defined by q-Analogue of Ruscheweyh Operator. Constr. Math. Anal. 3 (1)(2020), 36–44.
• Ş. Altınkaya, S. Yalçın: Upper bound of second Hankel determinant for bi-Bazilevic functions. Mediterr. J. Math. 13 (2016), 4081–4090.
• Ş. Altınkaya, S. Yalçın: On The Faber Polynomial Coefficient Bounds Of bi-Bazilevic Functions. Commun. Fac. Sci.Univ. Ank. Series A1 66 (2)(2017), 289–296.
• Ş. Altınkaya, S. Yalçın: On the Chebyshev polynomial coefficient problem of bi-bazilevic functions. TWMS J. App. Eng. Math. 10 (1)(2020), 251–258.
• D.A. Brannan and T.S. Taha, On some classes of bi-univalent functions, Studia Univ. Babeş-Bolyai Math., 31(1986), no. 2, 70-77.
• B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24(2011), no. 9, 1569--1573.
• P. Goswami, B. S. Alkahtani and T. Bulboac a, Estimate for initial MacLaurin coefficients of certain subclasses of bi-univalent functions, arXiv:1503.04644v1 [math.CV] March (2015).
• S. P. Goyal and P. Goswami, Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, J. Egyptian Math. Soc., 20(3)(2012), 179--182.
• M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18(1967), 63--68.
• Y. Li, K. Vijaya, G. Murugusundaramoorthy and H. Tang: On new subclasses of bi-starlike functions with bounded boundary rotation. AIMS Math. 5 (4)(2020), 3346–3356.
• M. Liu, On certain subclass of p-valent functions, Soochow J. Math., 20(2000), no. 2, 163-171.
• E. J. Moulis, Generalizations of the Robertson functions, Pacific J. Math., 81(1971), no. 1, 167-1174.
• G. Murugusundaramoorthy, T. Bulboaca: Estimate for initial MacLaurin coefficients of certain subclasses of bi-univalent functions of complex order associated with the Hohlov operator. Ann. Univ. Paedagog. Crac. Stud. Math. 17 (2018), 27–36.
• M. A. Nasr and M. K. Aouf, On convex functions of complex order, Mansoura Sci. Bull., 9(1982), 565--582.
• M. A. Nasr and M. K. Aouf, Starlike functions of complex order, J. Natur. Sci. Math., 25(1985), 1--12.
• M. A. Nasr and M. K. Aouf, Functions of bounded boundary rotation of complex order, Rev. Roum. Math. Pure Appl., 32(1987), no. 7, 623-629.
• K. Noor, M. Arif and A. Muhammad, Mapping properties of some classes of analytic functions under an integral operator, J. Math. Inequal., 4(2010), no. 4, 593-600.
• S. Owa, On certain Bazilevic functions of order β, Internat. J. Math. and Math. Sci., 15(1992), no. 3, 613-61.
• K.S. Padmanabhan and R. Parvatham, Properties of a class of functions with bounded boundary rotation, Ann. Polon. Math., 31 (1975), 311--323.
• B. Pinchuk, Functions with bounded boundary rotation, Israel J. Math., 10(1971), 7--16.
• M. S. Robertson, Variational formulas for several classes of analytic functions, Math. Z, 118 (1970), 311-319.
• H. M. Srivastava, A. K. Mishra and P.Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23(2010), 1188--1192.
• G. S. Salăgeăn, Subclasses of univalent functions, Lecture Notes in Math. (Springer-Verlag) 1013 , (1983), 362 - 372.
• T. M. Seoudy, On unified subclass of univalent functions of complex order involving the Salagean operator, J. Egyptian Math. Soc., 21(2013), no. 3, 194--196.
• T. M. Seoudy: Some results of certain class of multivalently Bavilevic functions. Konuralp J. Math. 8 (1)(2020), 21–29.
• T. S. Taha, Topics in univalent function theory, Ph. D. Thesis, University of London,1981.
• P. G. Umarani and M. K. Aouf, Linear combination of functions of bounded boundary rotation of order α, Tamkang J. Math., 20(1989), no. 1, 83-86.
• S. Yalçın, S. Khan and S. Hussain: Faber polynomial coefficients estimates of bi-univalent functions associated with generalized Salagean q-differential operator. Konuralp J. Math. 7 (1)(2020), 25–32.