Janowski Type q-Convex and q-Close-to-Convex Functions Associated with q-Conic Domain

Janowski type close-to-convex functions associated with conic regions

The analytic functions, mapping the open unit disk onto petal and oval type regions, introduced by Noor and Malik (Comput. Math. Appl. 62:2209-2217, 2011), are considered to define and study their associated close-to-convex functions. This work includes certain geometric properties like sufficiency criteria, coefficient estimates, arc length, the growth rate of coefficients of Taylor series, in...

Higher order close-to-convex functions associated with Attiya-Srivastava operator

In this paper‎, ‎we introduce a new class$T_{k}^{s,a}[A,B,alpha‎ ,‎beta ]$ of analytic functions by using a‎ ‎newly defined convolution operator‎. ‎This class contains many known classes of‎ ‎analytic and univalent functions as special cases‎. ‎We derived some‎ ‎interesting results including inclusion relationships‎, ‎a radius problem and‎ ‎sharp coefficient bound for this class‎.

COEFFICIENT ESTIMATES OF NEW CLASSES OF q–STARLIKE AND q–CONVEX FUNCTIONS OF COMPLEX ORDER

We introduce new classes of q -starlike and q -convex functions of complex order involving the q -derivative operator defined in the open unit disc. Furthermore, we find estimates on the coefficients for second and third coefficients of these classes.

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

ON CONVEX OPERATOR FOR (p, q)-ANALYTIC FUNCTIONS

We recall here some of the definitions given in [7]. Definition 1. The ’discrete plane’ Q′ with respect to some fixed point z′ = (x′, y′) in the first quadrant, is defined by the set of lattice points, Q′ = {(pmx′, qny′) : m,n ∈ Z the set of integers}. Definition 2. Two lattice points zi, zi+1 ∈ Q′ are said to be ’adjacent’ if zi+1 is one of (pxi, yi), (p−1xi, yi), (xi, qyi) or (xi, q−1yi). Def...