Abstract
The object of the present paper is to investigate the coefficients estimates, distortion properties, the radii of starlikeness and convexity, subordination theorems, partial sums and integral mean inequalities for classes of functions with two fixed points. Some remarks depicting consequences of the main results are also mentioned.MSC:30C45, 30C50, 30C55.
Highlights
Let M denote the class of functions which are holomorphic in D = D( ), whereD(r) = z ∈ C : < |z| < r .By M(p, k), where p, k are integer, p < k, we denote the class of functions f ∈ M of the form ∞f (z) = apzp + anzn (z ∈ D; ap > ). ( ) n=kWe note that for p < we have the class of functions which are meromorphic in U := U, Ur := Dr ∪ { }, and for p ≥ we obtain the class of functions which are analytic in U .Let p >, α ∈, p), r ∈
By W = W(p, k; φ, φ; A, B; δ) we denote the class of functions f ∈ M(p, k) such that (φ ∗ f )(z) = (z ∈ D)
The object of the present paper is to investigate the coefficients estimates, distortion properties, the radii of starlikeness and convexity, subordination theorems, partial sums and integral mean inequalities for the classes of functions with varying argument of coefficients
Summary
By T η(p, k), η ∈ R, we denote the class of functions f ∈ M(p, k) of the form We obtain the class T (p, k) of functions with negative coefficients. The object of the present paper is to investigate the coefficients estimates, distortion properties, the radii of starlikeness and convexity, subordination theorems, partial sums and integral mean inequalities for the classes of functions with varying argument of coefficients.
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