Abstract
In this paper, we consider the class of Bessel functions and the class of Struve functions. We obtain some univalence criteria for two general integral operators.
Highlights
Introduction and preliminariesLet consider U the unit disc
[4] If the function g is regular in U and | (z)| < 1 in U, for all ξ ∈ Uand z ∈ U the following inequalities hold (ξ) − (z) ≤ ξ − z 1 − (z) · (ξ) 1 − z · ξ
Theorem 1.5. [7],[9], [3] If v > −2 Re fv(z) < 0 for z ∈ U1(0, 4(v + 2)) and fv is univalent in U1(0, 4(v + 2))
Summary
Let H(U) be the set of holomorphic functions in the unit disc U. [1] If the function f is regular in unit disc U, f (z) = z + a2z2 + ... [4] If the function g is regular in U and | (z)| < 1 in U, for all ξ ∈ Uand z ∈ U the following inequalities hold (ξ) − (z) ≤ ξ − z 1 − (z) · (ξ) 1 − z · ξ (2). Let us consider the second-order inhomogeneous differential equation(([? The function Hv, which is called the Struve function of order v, is defined as a particular solution of (7).
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