Classes of uniformly starlike and convex functions

Abstract

Some classes of uniformly starlike and convex functions are introduced. The geometrical properties of these classes and their behavior under certain integral operators are investigated

Applications of a q-Salagean type operator on multivalent functions

“…(iii) For p = 1, m = 0, k = 0, and γ = 1 1-α , with 0 ≤ α < 1, the class k-US(q, γ , m, p) reduces to the class S * q (α) studied by Agrawal and Sahoo [2]. (iv) For p = 1, m = 0, q → 1, and γ = 1 1-α , with 0 ≤ α < 1, the class k-US(q, γ , m, p) reduces to the class SD(k, α) studied by Shams et al [28].…”

Fractional Calculus for Certain Integral Operator Involving Logarithmic Coefficients

“…Definition 4: A function f∈A is said to be in the class KD(µβ), if satisfies the following inequality [6] :…”

Some further properties for analytic functions with varying argument defined by Hadamard products

“…For suitable choices of φ, ψ and by specializing the parameters α, A, B involved in the class U (φ, ψ; α, A, B), we also obtain the following subclasses which were studied in many earlier works: [1] and Shams and Kulkarni [2]). …”

“…Let A denote the class of functions of the form 1) which are analytic in the open unit disc U = {z ∈ C : |z| < 1}. Let S be the subclass of A, consisting of analytic and univalent functions.…”

“…We denote by S * (β) and K(β) (0 ≤ β < 1) the class of starlike of order β in U and the class of convex functions of order β in U, respectively. It is well known that S * (β) ⊂ S * (0) = S * and K(β) ⊂ K(0) = K. A function f (z) ∈ A is said to be in U S(α, β), the class of α-uniformly starlike functions of order β (0 ≤ β < 1), if f satisfies the condition (see [1,2])…”