A Subclass of Analytic Functions Related tok-Uniformly Convex and Starlike Functions

Abstract

We investigate some subclasses of -uniformly convex and -uniformly starlike functions in open unit disc, which is generalization of class of convex and starlike functions. Some coefficient inequalities, a distortion theorem, the radii of close-to-convexity, and starlikeness and convexity for these classes of functions are studied. The behavior of these classes under a certain modified convolution operator is also discussed.

Coefficient Bounds for Certain Classes of Analytic Functions Associated with Faber Polynomial

“…From (25) and (26) we obtain the desired estimate of |a 2 | given by (16). Next, from (19) and 21, we have…”

“…Since Re w > α|w − 1| + γ if and only if Re{w(1 + αe iθ ) − αe iθ } > γ (see [19]), then the condition (5) is equivalent to…”

Multivalent Functions Related with an Integral Operator

“…For λ ∈ A p , given by (1), and using properties of gamma function, we have We also denote (1) for which arg(a t ) � π + (n − 1)η. For more details, see [15][16][17][18][19][20].…”