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

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

1. 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.
2. Altıntaş, O., Özkan, Ö ., Srivastava, H.M., Majorization by starlike functions of complex order, Complex Variables Theory Appl., 46(3)(2001), 207–218.
3. Bulut, S., Coefficient bounds for certain subclasses of analytic functions of complex order, Hacet. J. Math. Stat., 45(4)(2016), 1015–1022.
4. Bulut, S., Coefficient bounds for certain subclasses of close-to-convex functions of complex order, Filomat, 31(20)(2017), 6401–6408.
5. 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.
6. 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.
7. 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.
8. 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).

9. Robertson, M.S., On the theory of univalent functions, Ann. Math. (2), 37(2)(1936), 374–408.
10. Rogosinski, W., On the coefficients of subordinate functions, Proc. London Math. Soc. (Ser. 2), 48(1943), 48–82.
11. 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.
12. 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.
13. 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.
14. 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.
15. 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.
16. 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.