Abstract
Let f be the function defined on the open unit disk, with \(f(0)=0=f'(0)-1\), satisfying the subordinations \(zf'(z)/f(z)\prec \alpha + (1-\alpha )e^{z}\) or \(zf'(z)/f(z)\prec \alpha + (1-\alpha )\sqrt{1+ z}\) respectively, where \(0\le \alpha < 1\). The sharp radii has been determined for these functions to belong to several well-known classes. In addition, some inclusion relations and coefficient estimates are also obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ali, R.M., Ravichandran, V., Seenivasagan, N.: Coefficient bounds for \(p\)-valent functions. Appl. Math. Comput. 187(1), 35–46 (2007)
Kanas, S., Wisniowska, A.: Conic regions and \(k\)-uniform convexity. J. Comput. Appl. Math. 105(1–2), 327–336 (1999)
Kanas, S., Wiśniowska, A.: Conic domains and starlike functions. Rev. Roum. Math. Pures Appl. 45(4), 647–657 (2000)
Ma, W.C., Minda, D.: A unified treatment of some special classes of univalent functions. In: Proceedings of the Conference on Complex Analysis (Tianjin, 1992), Conf. Proc. Lecture Notes Anal., I, pp. 157–169. Int. Press, Cambridge
Mendiratta, R., Nagpal, S., Ravichandran, V.: On a subclass of strongly starlike functions associated with exponential function. Bull. Malays. Math. Sci. Soc. 38(1), 365–386 (2015)
Padmanabhan, K.S., Parvatham, R.: Some applications of differential subordination. Bull. Austr. Math. Soc. 32(3), 321–330 (1985)
Robertson, M.S.: Certain classes of starlike functions. Mich. Math. J. 32(2), 135–140 (1985)
Shanmugam, T.N.: Convolution and differential subordination. Int. J. Math. Math. Sci. 12(2), 333–340 (1989)
Sokól, J.: Radius problems in the class \(\cal{S}^*_{L}\). Appl. Math. Comput. 214(2), 569–573 (2009)
Sokól, J., Stankiewicz, J.: Radius of convexity of some subclasses of strongly starlike functions. Zeszyty Nauk. Politech. Rzeszowskiej Mat. No. 19, 101–105 (1996)
Uralegaddi, B.A., Ganigi, M.D., Sarangi, S.M.: Univalent functions with positive coefficients. Tamkang J. Math. 25(3), 225–230 (1994)
Author information
Authors and Affiliations
Corresponding author
Additional information
The authors are thankful to the referees for their useful comments.
Rights and permissions
About this article
Cite this article
Khatter, K., Ravichandran, V. & Kumar, S.S. Starlike functions associated with exponential function and the lemniscate of Bernoulli. RACSAM 113, 233–253 (2019). https://doi.org/10.1007/s13398-017-0466-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13398-017-0466-8