Carlson and Shaffer [B.C. Carlson, D.B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984) 737–745] have introduced a linear operator associated with the Gaussian hypergeometric function which has been generalized by Dziok and Srivastava [J. Dziok, H.M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl....

We investigate the new class H b (α, β) of analytic functions with Koebe type. The subordination, superordination, best dominant result for that class was obtain. And by making use of Jack's Lemma as well as several differential and other inequalities, the authors derive sufficient conditions for starlikeness of the class H b (α, β) of n-fold symmetric analytic functions of Koebe type. Relevant...

We determine the sufficient conditions for subordination for new classes of normalized analytic functions with applications in fractional calculus in complex domain. 2010 Mathematics Subject Classification: 34G10, 26A33, 30C45.

We obtain some subordination and superordination results involving the generalized Sălăgean differential operator for certain normalized analytic functions in the open unit disk. Our results extend corresponding previously known results.

In this paper, we introduce a new class of analytic functions defined by a new convolution operator La (α, β). The new class of analytic functions Σ a,t α,β (ρ; h) in U ∗ = {z : 0 < |z| < 1} is defined by means of a hypergeometric function with an integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination. The authors also introduces and investigates variou...

Let the functions q1 be analytic and let q2 be analytic univalent in the unit disk. Using the methods of differential subordination and superordination, sufficient conditions involving the Schwarzian derivative of a normalized analytic function f are obtained so that either q1 z ≺ zf ′ z /f z ≺ q2 z or q1 z ≺ 1 zf ′′ z /f ′ z ≺ q2 z . As applications, sufficient conditions are determined relati...

In [4], under some easy to remove genericity assumptions, we proved the analytic subordination of the Cauchy transforms of distributions GμX+Y and GμX for a pair of freely independent self-adjoint random variables X, Y . We used this to obtain inequalities among p-norms of densities of distributions, free entropies and Riesz energies. This was followed by P.Biane’s discovery [1] that subordinat...

In the present paper, we investigate some subordination and superordination preserving properties of analytic functions associated with the Srivastava-Khairnar-More integral operator defined on the space of normalized analytic functions in the open unit disk U. Several sandwich-type results associated with this transformation are derived. Some useful consequences of the main results are mention...

We introduce the analytic functions f (z) = z + ∞ ∑ k=n+1 akz k ( n ∈ N) and p(z) = z + m ∑ s=1 bsj−s+1zsj−s+1 (j ≥ n + 1;n ∈ N) in the open unit disk U. By means of the subordination theorem of J.E. Littlewood, we shall investigate the integral means with coefficients inequalities of analytic functions f(z) and p(z). Some applications of the integral mean of f(z) are considered. 2000 Mathemati...