Sufficient conditions and radius problems for the Silverman class - Kumar, S. Sivaprasad; Priyanka, Priyanka (Ukrains’kyi Matematychnyi Zhurnal, 2024)
UDC 517.5 For 0<α≤1 and λ>0, let equation1 G_λ,α={fA|1-α+α zf’’(z)/f’(z)z f’(z)/f(z)-(1-α)|<λ, zD}.0.1equation The general form of the Silverman class introduced by Tuneski and Irmak [Int. J. Math. and Math. Sci., 2006, Article ID 38089 (2006)]. Our differential inequality formulation lays out several sufficient conditions for this class. Further, we consider a class Ω given by equationomegaΩ={fA|zf’(z)-f(z)|<12, zD}.0.2equation For these two classes, we establish inclusion relations involving some well-known subclasses of S^* and compute radius estimates featuring various pairings of these classes.