Abstract
The main object of the present paper is to investigate a number of useful properties such as
sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikness and radius of convexity for
a new subclass of meromorphic convex functions, which are defined here by means of a newly defined q-linear
differential operator.
Results & Lemmas (5)
Each result is auto-extracted from the paper via OCR - the math is shown verbatim and may carry occasional transcription artifacts. Click to expand the full statement.
Theorem 2.1.
Theorem 2.1. Let f ∈Ap be of the form (1.1) and satisfy the inequality ∞ X n=1 qp[n+p,q][µ+1,q]n+p [n+p,q]! (qp[n + p, q] (1 + B) + (1 + A)…
Theorem 2.1. Let f ∈Ap be of the form (1.1) and satisfy the inequality ∞ X n=1 qp[n+p,q][µ+1,q]n+p [n+p,q]! (qp[n + p, q] (1 + B) + (1 + A) [p, q]) |an+p| ≤ [p, q]2 (A −B) . (2.1) Then the function f ∈MC∗ q (p, µ, A, B) .
Theorem 2.2.
Theorem 2.2. Let f ∈MC∗ q (p, µ, A, B) and has the form (1.1). Then for |z| = r 1 rp −τ1rp ≤|f(z)| ≤1 rp + τ1rp, where τ1 = (A −B) [p, q]!…
Theorem 2.2. Let f ∈MC∗ q (p, µ, A, B) and has the form (1.1) . Then for |z| = r 1 rp −τ1rp ≤|f(z)| ≤1 rp + τ1rp, where τ1 = (A −B) [p, q]! [p, q]2 qp[µ + 1, q]p+1((1 + A) [p, q] + qp[p + 1, q] (1 + B)).
Theorem 2.3.
Theorem 2.3. Let f ∈MC∗ q (p, µ, A, B) and has the form (1.1). Then for |z| = r [p, q]m qmp+ζrm+p −τ2rp ≤ ∂m q f(z) ≤ [p, q]m qmp+ζrm+p +…
Theorem 2.3. Let f ∈MC∗ q (p, µ, A, B) and has the form (1.1) . Then for |z| = r [p, q]m qmp+ζrm+p −τ2rp ≤ ∂m q f(z) ≤ [p, q]m qmp+ζrm+p + τ2rp. where τ2 = [p, q]2 (A −B) [p, q]! ((1 + A) [p, q] + qp[p + 1, q] (1 + B)) and ζ = m X
Theorem 2.4.
Theorem 2.4. Let f ∈MC∗ q (p, µ, A, B). Then f ∈MCp (α) for |z| < r1, where r1 =
Theorem 2.4. Let f ∈MC∗ q (p, µ, A, B) . Then f ∈MCp (α) for |z| < r1, where r1 =
Theorem 2.5.
Theorem 2.5. Let f ∈MC∗ q (p, µ, A, B). Then f ∈MS∗ p (α) for |z| < r2, where r2 =
Theorem 2.5. Let f ∈MC∗ q (p, µ, A, B). Then f ∈MS∗ p (α) for |z| < r2, where r2 =
Function classes studied:
Related Papers