Fekete-Szegö Inequality for Certain Subclasses of Analytic Functions Defined by The Combination of Differential and Integral Operators

Year 2023, Volume: 13 Issue: 3, 2093 - 2104, 01.09.2023

Sercan Kazımoğlu

https://doi.org/10.21597/jist.1273661

Abstract

In this paper, we introduced certain general new subclasses of analytic functions defined by the combination of two special operator which one of them derivative (Deniz-Orhan derivative operator) and other integral (Noor integral operators). For these classes coefficient estimates and the Fekete–Szegö inequality is completely solved.

Keywords

Fekete-Szegö inequality , Starlike and convex functions of complex order , Noor integral operator , Analytic functions

References

• Abdel-Gawad, H. R. and Thomas, D. K. (1992). The Fekete-Szegö problem for strongly close-to-convex functions. Proc. Am. Math. Soc., 114, 345-349.
• Al-Oboudi, F. M. (2004). On univalent functions defined by a generalized Sălăgean operator. Int. J. Math. Math. Sci., 27, 1429–1436.
• Chonweerayoot, A., Thomas, D. K. and Upakarnitikaset, W. (1992). On the Fekete-Szegö theorem for close-to-convex functions. Publ. Inst. Math. (Beograd) (N.S.), 66, 18-26.
• Çağlar, M. and Orhan, H. (2021). Fekete-Szegö problem for certain subclasses of analytic functions defined by the combination of differential operators. Bol. Soc. Mat. Mex., 27, 41.
• Darus, M. and Thomas, D. K. (1996). On the Fekete-Szegö theorem for close-to-convex functions. Math. Jpn., 44, 507–511.
• Darus, M. and Thomas, D. K. (1998). On the Fekete-Szegö theorem for close-to-convex functions. Math. Jpn., 47, 125–132.
• Deniz, E. and Orhan, H. (2010). The Fekete-Szegö problem for a generalized subclass of analytic functions. Kyungpook Math. J., 50, 37–47.
• Deniz, E., Çağlar, M. and Orhan, H. (2012). The Fekete-Szegö problem for a class of analytic functions defined by Dziok-Srivastava operator. Kodai Math. J., 35, 439–462.
• Fekete, M. and Szegö, G. (1933). Eine Bemerkung u¨ber ungerade schlichte Funktionen. J. Lond. Math. Soc., 8, 85–89.
• Kanas, S. and Darwish, H. E. (2010). Fekete-Szegö problem for starlike and convex functions of complex order. Appl. Math. Lett., 23(7), 777–782.
• Kazımoğlu, S. and Deniz, E., (2020). Fekete-Szegö problem for generalized bi-subordinate functions of complex order. Hacettepe Journal of Mathematics and Statistics, 49(5), 1695-1705.
• Kazımoğlu, S. and Mustafa, N., (2020). Bounds for the initial coefficients of a certain subclass of bi-univalent functions of complex order. Palestine Journal of Mathematics, 9(2), 1020-1031.
• Keogh, F. R. and Merkes, E. P. (1969). A coefficient inequality for certain classes of analytic functions. Proc. Am. Math. Soc., 20, 8–12.
• Koepf, W. (1987). On the Fekete-Szegö problem for close-to-convex functions. Proc. Am. Math. Soc., 101, 89–95.
• London, R. R. (1993). Fekete-Szegö inequalities for close-to-convex functions. Proc. Am. Math. Soc., 117, 947–950.
• Ma, W. and Minda, D. (1994). A unified treatment of some special classes of univalent functions. In: Li, Z., Ren, F., Yang, L. and Zhang, S. (eds.) Proceeding of the International Conference on Complex Analysis, 157–169. Int. Press, Boston.
• Nasr, M. A. and Aouf, M. K. (1985). Starlike function of complex order. J. Nat. Sci. Math., 25, 1–12.
• Nasr, M. A. and Aouf, M. K. (1982). On convex functions of complex order. Mansoura Sci. Bull., 8, 565–582.
• Noor, K. I. (1999). On new classes of integral operators. J. Nat. Geometry, 16, 71-80.
• Orhan, H., Deniz, E. and Çağlar, M. (2012). Fekete-Szegö problem for certain subclasses of analytic functions. Demonstr. Math., 45(4), 835–846.
• Orhan, H., Deniz, E. and Răducanu, D. (2010). The Fekete-Szegö problem for subclasses of analytic functions defined by a differential operator related to conic domains. Comput. Math. Appl., 59, 283–295.
• Orhan, H. and Răducanu, D. (2009). Fekete-Szegö problem for strongly starlike functions associated with generalized hypergeometric functions. Math. Comput. Model., 50, 430–438.
• Pfluger, A. (1984). The Fekete-Szegö inequality by a variational method. Ann. Acad. Sci. Fenn. Ser. AI, 10, 447–454.
• Pommerenke, C. (1975). Univalent functions. In: Studia Mathematica Mathematische Lehrbucher, Vandenhoeck and Ruprecht, Göttingen.
• Răducanu, D. and Orhan, H. (2010). Subclasses of analytic functions defined by a generalized differential operator. Int. J. Math. Anal., 4(1), 1–15.
• Ruscheweyh, S. (1975). New criteria for univalent functions. Proc. Am. Math. Soc., 49, 109–115.
• Sălăgean, G. S. (1983). Subclasses of univalent functions. In: Complex analysis–Proc. 5th Rom.-Finn. Semin., Bucharest 1981, Part 1, Lect. Notes Math. 1013, 362-372.
• Sokol, J. and Bansal, D. (2012). Coefficients bounds in some subclass of analytic functions. Tamkang Journal of Mathematics, 43(4), 621–630.
• Wiatrowski, P. (1971). The coefficients of a certain family of holomorphic functions. Zeszyty Nauk. Uniw. Lodz., Nauki. Mat. Przyrod. Ser. II, 39, 75–85.