## A certain subclass of analytic and close-to-convex functions.(English)Zbl 1206.30035

Summary: We introduce and investigate an interesting subclass $$\mathcal K_s(h)$$ of close-to-convex analytic functions in the open unit disk $$\mathbb U$$. For functions belonging to the class $$\mathcal K_s(h)$$, we derive several properties including (for example) coefficient bounds as well as distortion and growth theorems. The various results presented here generalize many known results.

### MSC:

 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
Full Text:

### 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, 1218-1222, (2007) · Zbl 1139.30005 [2] Altıntaş, O.; Özkan, Ö.; Srivastava, H.M., Neighborhoods of a class of analytic functions with negative coefficients, Appl. math. lett., 13, 3, 63-67, (1995) · Zbl 0955.30015 [3] Breaz, D.; Breaz, N.; Srivastava, H.M., An extension of the univalent condition for a family of integral operators, Appl. math. lett., 22, 41-44, (2009) · Zbl 1163.30304 [4] Owa, S.; Nunokawa, M.; Saitoh, H.; Srivastava, H.M., Close-to-convexity, starlikeness, and convexity of certain analytic functions, Appl. math. lett., 15, 63-69, (2002) · Zbl 1038.30011 [5] Gao, C.; Zhou, S., On a class of analytic functions related to the starlike functions, Kyungpook math. J., 45, 123-130, (2005) · Zbl 1085.30015 [6] Kowalczyk, J.; Leś-Bomba, E., On a subclass of close-to-convex functions, Appl. math. lett., (2010) · Zbl 1193.30018 [7] 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, 763-768, (2010) · Zbl 1189.30041 [8] Robertson, M.S., On the theory of univalent functions, Ann. of math. (1), 37, 374-408, (1936) · JFM 62.0373.05 [9] Duren, P.L., () [10] () [11] Miller, S.S.; Mocanu, P.T., () [12] Rogosinski, W., On the coefficients of subordinate functions, Proc. London math. soc. (2), 48, 48-82, (1943) · Zbl 0028.35502
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.