Stability for the class of uniformly starlike functions with respect to symmetric points. (English) Zbl 1298.30008
Summary: In this paper we investigate the problem of stability for the class of uniformly starlike functions with respect to symmetric points and we give the lower bounds of their radius of stability.
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 30C80 | Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination |
References:
| [1] | Bednarz, U., Sokół, J.: On order of convolution consistence of the analytic functions. Studia Univ. Babeş-Bolyai Math. 3, 41-50 (2010) · Zbl 1240.30037 |
| [2] | Bednarz, U., Kanas, S.: Stability of the integral convolution of k-uniformly convex and k-starlike functions. J. Appl. Anal. 10(1), 105-115 (2004) · Zbl 1067.30018 · doi:10.1515/JAA.2004.105 |
| [3] | 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 |
| [4] | Kanas, S.: Stability of convolution and dual sets for class of k-uniformly convex and \[k\] k-starlike functions. Folia Sci. Univ. Tech. Resov. 22, 51-63 (1998) · Zbl 0995.30014 |
| [5] | Ma, W., Minda, D.: Uniformly convex functions. Ann. Polon. Math. 57, 165-175 (1992) · Zbl 0760.30004 |
| [6] | Padmanabhan, K.S.: On uniformly convex functions in the unit disc. J. Anal. 2, 87-96 (1994) · Zbl 0805.30009 |
| [7] | Parvatham, R., Premabi, M.: Neighbourhoods of uniformly starlike functions with respect to symmetric points. Bull. Cal. Math. Soc. 88, 155-16 (1996) · Zbl 0879.30005 |
| [8] | Ram Reddy, T., Thirupathi Reddy, P.: Neighbourhood of a certain subclasses of \[SP(\beta )\] SP(β). In: Procedings of the International Conference on Geometric Function Theory, Special Functions and Applications (ICGFT), vol. 15, pp. 239-245 (2007) · Zbl 1185.30017 |
| [9] | Rønning, F.: Uniformly convex functions and a corresponding class of starlike functions. Proc. Am. Math. Soc. 118, 189-196 (1993) · Zbl 0805.30012 |
| [10] | Rønning, F.: Integral representatios of bounded starlike functions. Ann. Polon. Ann. Polon. Math. 60, 289-297 (1995) · Zbl 0818.30008 |
| [11] | Ruscheweyh, S.T.: Duality for hadmarad product with applications to extremal problems. Trans. Am. 210, 63-74 (1975) · Zbl 0311.30011 |
| [12] | Ruscheweyh, S.T.: Neighbourhoods of univalent functions. Proc. Am. Math. Soc. 81, 521-527 (1981) · Zbl 0458.30008 |
| [13] | Ruscheweyh, S.T., Sheil-Small, T.: Hadamard products of schlicht functions and the Pólya-Schoenberg. Comment. Math. Helv. 48, 119-135 (1973) · Zbl 0261.30015 |
| [14] | Sakaguchi, K.: On a certain univalent functions. J. Math. Soc. Jpn. 11, 72-80 (1959) · Zbl 0085.29602 · doi:10.2969/jmsj/01110072 |
| [15] | Xu, Q.H., Wu, G.P.: Coefficient estimate for a subclass of univalent functions with respect to symmetric points. EJPAM 3(6), 1055-1061 (2010) · Zbl 1213.30043 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
