Coefficient bounds for the General Subclasses of Close-to-Convex Functions of Complex Order

Year 2024, Volume: 16 Issue: 1, 162 - 168, 30.06.2024

Serap Bulut

https://doi.org/10.47000/tjmcs.1338657

Abstract

In this study, we introduce two new subclasses of close-to-convex functions of complex order, which
are introduced here by means of a certain non-homogenous Cauchy-Euler-type differential equation of order m, and determine the coefficient bounds for functions belonging to these new classes.

Keywords

Analytic function , close-to-convex function , non-homogeneous Cauchy-Euler differential equation

References

• Altıntaş, O., Irmak, H., Owa, S., Srivastava, H.M., Coefficient bounds for some families of starlike and convex functions of complex order, Appl. Math. Lett., 20(2007), 1218–1222.
• Altıntaş, O., Özkan, Ö ., Srivastava, H.M., Majorization by starlike functions of complex order, Complex Variables Theory Appl., 46(3)(2001), 207–218.
• Bulut, S., Coefficient bounds for certain subclasses of analytic functions of complex order, Hacet. J. Math. Stat., 45(4)(2016), 1015–1022.
• Bulut, S., Coefficient bounds for certain subclasses of close-to-convex functions of complex order, Filomat, 31(20)(2017), 6401–6408.
• Faisal, I., Darus, M., Application of nonhomogenous Cauchy-Euler differential equation for certain class of analytic functions, Hacet. J. Math. Stat., 43(3)(2014), 375–382.
• Murugusundaramoorthy, G., Srivastava, H.M., Neighborhoods of certain classes of analytic functions of complex order, J. Inequal. Pure Appl. Math., 5(2)(2004), 1–8.
• Nasr, M.A., Aouf, M.K., Radius of convexity for the class of starlike functions of complex order, Bull. Fac. Sci. Assiut Univ. A, 12(1)(1983), 153–159.
• Orhan, H., R˘aducanu, D., C¸ a˘glar, M., Bayram, M., Coefficient estimates and other properties for a class of spirallike functions associated with a differential operator, Abstr. Appl. Anal., (2013).
• Robertson, M.S., On the theory of univalent functions, Ann. Math. (2), 37(2)(1936), 374–408.
• Rogosinski, W., On the coefficients of subordinate functions, Proc. London Math. Soc. (Ser. 2), 48(1943), 48–82.
• Srivastava, H.M., Altıntas¸, O., Kırcı Serenbay, S., Coefficient bounds for certain subclasses of starlike functions of complex order, Appl. Math. Lett., 24(2011), 1359–1363.
• Srivastava, H.M., Xu, Q.-H.,Wu, G.-P., Coefficient estimates for certain subclasses of spiral-like functions of complex order, Appl. Math. Lett., 23(2010), 763–768.
• Ul-Haq, W., Nazneen, A., Rehman, N., Coefficient estimates for certain subfamilies of close-to-convex functions of complex order, Filomat, 28(6)(2014), 1139–1142.
• Ul-Haq, W., Nazneen, A., Arif, M.,Rehman, N., Coefficient bounds for certain subclasses of close-to-convex functions of Janowski type, J. Comput. Anal. Appl., 16(1)(2014), 133–138.
• Xu, Q.-X., Cai, Q.-M., Srivastava, H.M., Sharp coefficient estimates for certain subclasses of starlike functions of complex order, Appl. Math. Comput., 225(2013), 43–49.
• Xu, Q.-H., Gui, Y.-C., Srivastava, H.M., Coefficient estimates for certain subclasses of analytic functions of complex order, Taiwanese J. Math., 15(5)(2011), 2377–2386.