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The estimates for the second Hankel determinant a 2 a 4 – a 2 3 of the analytic function f (z) = z + a 2 z 2 + a 3 z 3 + · · · , for which either zf (z)/f (z) or 1 + zf (z)/f (z) is subordinate to a certain analytic function, are investigated. The estimates for the Hankel determinant for two other classes are also obtained. In particular, the estimates for… (More)
The general classes of multivalent starlike, convex, close-to-convex and quasi-convex functions are introduced. These classes provide a unified treatment to various known subclasses. Inclusion and convolution properties are derived using the methods of convex hull and differential subordination.
In this paper, we obtain some sufficient conditions for an analytic function f (z), defined on the unit disk , to be starlike of order α.
Estimates on the initial coefficients are obtained for normalized analytic functions f in the open unit disk with f and its inverse g = f −1 satisfying the conditions that zf ′ (z)/f (z) and zg ′ (z)/g(z) are both subordinate to a starlike univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are… (More)
Sharp bounds for ja pþ2 À la 2 pþ1 j and ja p+3 j are derived for certain p-valent analytic functions. These are applied to obtain Fekete-Szegö like inequalities for several classes of functions defined by convolution.
In this paper we give certain sufficient conditions for functions defined through the Dziok-Srivastava linear operator and the multiplier transformation .
In the present investigation, the authors derive necessary and sufficient conditions for spirallikeness and convex spirallikeness of a suitably normalized meromorphic p-valent function in the punctured unit disk, using convolution. Also we give an application of our result to obtain a convolution condition for a class of meromorphic functions defined by a… (More)
In the present investigation, we obtain certain sufficient conditions for a normalized analytic function f(z) defined by the Dziok–Srivastava linear operator H l m ½a 1 to satisfy the certain subordination. Our results extend corresponding previously known results on starlikeness, convexity, and close to convexity.