Abstract
Certain results on starlike and convex functions
Highlights
Let T (p) denote the class of functions f of the form ∞ f (z) = zp + ∑ akzk, where p ∈ N = {1, 2, 3, . . . }, k=p+1 which are analytic and p−valent in the open unit disk E = {z ∈ C : |z| < 1} in the complex plane C
We write S1∗(0) = S∗ and K1(0) = K, where S∗ and K are the usual subclasses of T (= T (1)) consisting of functions which are starlike and convex respectively
Let Φ : C2 × E → C be an analytic function, p be an analytic function in E with (p(z), zp (z); z) ∈ C2 × E
Summary
In most of the results obtained here, the region of variability of the differential operators implying starlikeness and convexity of analytic functions has been extended. Let q be a univalent function in E, with q(z) = {0, p}, p ∈ N and satisfying the following condition
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