We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
NEW RESULTS RELATED TO THE CONVEXITY OF INTEGRAL OPERATOR.
- Authors
Panigrahi, Trailokya
- Abstract
Let U be the open unit disk in the complex plane ℂ. Let H[U] be the class of holomorphic functions in U. For a ∈ ℂ and n ∈ ℕ : = {1,2,3,...}, let H[a,n] = {f ∈ H[U] : f(z) = a + anzn + an+1zn+1 + ....(z ∈ U)}, and An = {f ∈ H[U] : f(z) = z + an+1zn+1 + ....(z ∈ U)} . In the present paper, the author determines the sufficient condition for the function f ∈ An defined on the open unit disk U such that image of f under the integral operator Iμ,βn(f)(z) = (β + μ/n/ zμ/n ∫0z tμ/n-1 fβ(t)dt)1/β is convex univalent function. We also determine the sufficient condition for the function class H(1,1) . Our result extends the corresponding previously known results.
- Subjects
ANALYTIC functions; STAR-like functions; INTEGRAL operators
- Publication
Palestine Journal of Mathematics, 2016, Vol 5, Issue 2, p270
- ISSN
2219-5688
- Publication type
Article