Sufficient conditions for starlikeness associated with parabolic region. (2002)

• Record Type: Journal Article
• Authors: Ravichandran, V.; Gangadharan, A.; Shanmugam, T. N.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 32:Number 5(2002)
• Page Start: 319
• Page End: 324
• Publication Date: 2002
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171202007895
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : An analytic functionf ( z ) = z + a n + 1 z n + 1 + ⋯, defined on the unit disk△ = { z : | z | < 1 }, is in the classS p ifz f ′ ( z ) / f ( z ) is in the parabolic regionRe w > | w − 1 | . This class is closely related to the class of uniformly convex functions. Sufficient conditions for function to be inS p are obtained. In particular, we find condition onλ such that the functionf ( z ), satisfying( 1 − α ) ( f ( z ) / z ) μ + α f ′ ( z ) ( f ( z ) / z ) μ − 1 ≺ 1 + λ z, is inS p .