Abstract. In this paper we introduce a new subclass Mp(n, α, c) of analytic and multivalent functions in the unit disk which includes the class Sp(n, α) of multivalent starlike functions of order α and the class Tp(n,α) of multivalent convex functions of order α . Using generalized Bernardi Libera integral operator and Hölder’s inequality, some interesting properties of convolution for the clas...

In [6] it was shown that if f ∈ is starlike of order α, α= 0.294, . . . , so is the Libera integral operator F . We also know that (see, e.g., [1]) there are functions which are univalent or spiral-like in so that their Libera integral operators are not univalent or spiral-like in . Li and Owa [5] proved that if f ∈ is univalent in , then Fn(z) is starlike in |z| < 3/8. The number 3/8 is sharp....

The results contained in this paper are the result of a study regarding fractional calculus combined with classical theory differential subordination established for analytic complex valued functions. A new operator is introduced by applying Libera integral and order λ Many properties obtained newly defined using famous lemmas proved important scientists concerned geometric function theory, suc...

Many papers concern both the starlikeness and convexity of Bernardi integral operator. Using Nunokawa’s Lemma, we want to determine conditions for strong transform normalized analytic functions g, such that |arg{g′(z)}| &lt;απ2 in open unit disk Δ where 0&lt;α&lt;2. Our results include Mocanu, Nunokawa others on Libera transform.

ON THE REAL PART OF A CLASS OF ANALYTIC FUNCTIONS B.A. Frasin Abstract. Let T (β, b), β(β ≥ 0) and b ∈ C denote the class of analytic functions f(z) in the open unit disk which satisfy the condition Re {f ′(z) + βzf ′′(z)} > 1 − |b| . Inclusion relations of functions in the class T (β, b) are given. Lower bounds are also obtained for the n-th partial sums Fn(z) of the Libera integral operator F...