Fekete-Szegö Problem for Certain Subclass of Analytic Functions with Complex Order Defined by q-Analogue of Ruscheweyh Operator
Year 2020,
, 36 - 44, 01.03.2020
Tamer Seoudy
,
Mohamed Kamal Aouf
Abstract
In this paper, we study Fekete-Szegö Problem for certain subclass of analytic functions with complex order in the open unit disk by applying the q-analogue of Ruscheweyh operator in conjunction with the principle of subordination between analytic functions.
References
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- H. Aldweby and M. Darus, Coefficient estimates of classes of q-starlike and q-convex functions, Advanced Studies in Contemporary Math., 26(2016), no. 1, 21-26.
- H. Aldweby and M. Darus, On Fekete-Szegö problems for certain subclasses defined by q-derivative, J. Function Spaces, Vol. 2017, Art. ID 7156738, 1-5, 2017.
- F. M. Al-Oboudi and M. M. Haidan, Spirallike functions of complex order, J. Natur. Geom., 19(2000), 53-72.
- M. K. Aouf, F. M. Al-Oboudi and M. M. Haidan, On some results for λ-spirallike and λ-Robertson functions of complex order, Publ. Instit. Math. Belgrade, 77(2005), no. 91, 93-98.
- A. Aral, V. Gupta, and R. P.Agarwal, Applications of q-Calculus in Operator Theory, Springer, New York, USA, 2013.
- T. Bulboacă, Differential Subordinations and Superordinations, Recent Results, House of Scientific Book Publ., Cluj-Napoca, 2005.
- B. A. Frasin, Family of analytic functions of complex order, Acta Math. Acad. Paedagog. Nyházi. (N. S.), 22(2006), no.2, 179-191.
- F. H. Jackson, On q-definite integrals, Quarterly J. Pure Appl. Math., 41(1910), 193--203.
- F. H. Jackson, On q-functions and a certain difference operator, Transactions of the Royal Society of Edinburgh, 46(1908), 253--281.
- W. C. Ma and D. Minda, A unified treatment of some special classes of univalent functions, in Proceedings of the Conference on Complex Analysis (Tianjin, 1992), 157--169, Internat. Press, Cambridge, MA.
- S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker, New York and Basel, 2000.
- M. A. Nasr and M. K. Aouf, On convex functions of complex order, Mansoura Bull. Sci., 8(1982), 565--582.
- M. A. Nasr and M. K. Aouf, Starlike function of complex order, J. Natur. Sci. Math., 25(1985), 1--12.V. Ravichandran, Yasar Polatoglu, Metin Bolcal and Arsu Sen, Certain subclasses of starlike and convex functions of complex order, Hacettepe J. Math. Stat., 34(2005), 9-15.
- V. Ravichandran, Y. Polatoglu, M. Bolcal and A. Sen: Certain subclasses of starlike and convex functions of complex
order. Hacettepe J. Math. Stat. 34 (2005), 9-15.
- St. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc., 49(1975), 109--115.
- M. S. Robertson, On the theory of univalent functions, Ann. Math., 37(1936), 374- 408.
- T. M. Seoudy and M. K. Aouf, Coefficient estimates of new classes of q-starlike and q-convex functions of complex order, J. Math. Inequal., 10 (2016), 135-145.
- P. Wiatrowski, On the coefficients of some family of holomorphic functions, Zeszyty Nauk. Uniw. Łódz, Nauk. Mat.-Przyr., 39(1970), 75--85.
Year 2020,
, 36 - 44, 01.03.2020
Tamer Seoudy
,
Mohamed Kamal Aouf
References
- H. Aldweby and M. Darus, Some subordination results on q-analogue of Ruscheweyh differential operator, Abstract and Applied Analysis, vol. 2014,Art. ID 958563, 1-6, 2014.
- H. Aldweby and M. Darus, Coefficient estimates of classes of q-starlike and q-convex functions, Advanced Studies in Contemporary Math., 26(2016), no. 1, 21-26.
- H. Aldweby and M. Darus, On Fekete-Szegö problems for certain subclasses defined by q-derivative, J. Function Spaces, Vol. 2017, Art. ID 7156738, 1-5, 2017.
- F. M. Al-Oboudi and M. M. Haidan, Spirallike functions of complex order, J. Natur. Geom., 19(2000), 53-72.
- M. K. Aouf, F. M. Al-Oboudi and M. M. Haidan, On some results for λ-spirallike and λ-Robertson functions of complex order, Publ. Instit. Math. Belgrade, 77(2005), no. 91, 93-98.
- A. Aral, V. Gupta, and R. P.Agarwal, Applications of q-Calculus in Operator Theory, Springer, New York, USA, 2013.
- T. Bulboacă, Differential Subordinations and Superordinations, Recent Results, House of Scientific Book Publ., Cluj-Napoca, 2005.
- B. A. Frasin, Family of analytic functions of complex order, Acta Math. Acad. Paedagog. Nyházi. (N. S.), 22(2006), no.2, 179-191.
- F. H. Jackson, On q-definite integrals, Quarterly J. Pure Appl. Math., 41(1910), 193--203.
- F. H. Jackson, On q-functions and a certain difference operator, Transactions of the Royal Society of Edinburgh, 46(1908), 253--281.
- W. C. Ma and D. Minda, A unified treatment of some special classes of univalent functions, in Proceedings of the Conference on Complex Analysis (Tianjin, 1992), 157--169, Internat. Press, Cambridge, MA.
- S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker, New York and Basel, 2000.
- M. A. Nasr and M. K. Aouf, On convex functions of complex order, Mansoura Bull. Sci., 8(1982), 565--582.
- M. A. Nasr and M. K. Aouf, Starlike function of complex order, J. Natur. Sci. Math., 25(1985), 1--12.V. Ravichandran, Yasar Polatoglu, Metin Bolcal and Arsu Sen, Certain subclasses of starlike and convex functions of complex order, Hacettepe J. Math. Stat., 34(2005), 9-15.
- V. Ravichandran, Y. Polatoglu, M. Bolcal and A. Sen: Certain subclasses of starlike and convex functions of complex
order. Hacettepe J. Math. Stat. 34 (2005), 9-15.
- St. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc., 49(1975), 109--115.
- M. S. Robertson, On the theory of univalent functions, Ann. Math., 37(1936), 374- 408.
- T. M. Seoudy and M. K. Aouf, Coefficient estimates of new classes of q-starlike and q-convex functions of complex order, J. Math. Inequal., 10 (2016), 135-145.
- P. Wiatrowski, On the coefficients of some family of holomorphic functions, Zeszyty Nauk. Uniw. Łódz, Nauk. Mat.-Przyr., 39(1970), 75--85.