Abstract
In this paper, the k-integral operators for analytic functions dened in the open unit disc U = fz 2 C : jzj < 1g are introduced. Several new subclasses of analytic functions satisfying certain relations involving these operators are also introduced. Further, we establish the inclusion relation for these subclasses. Next, the integral preserving properties of a k-integral operator satised by these newly introduced subclasses are obtained. Some applications of the results are discussed. Concluding remarks are also given.
Highlights
The k-integral operators for analytic functions dened in the open unit disc U = {z ∈ C : |z| < 1} are introduced
Geometric function theory is one of the most important branches of complex analysis which focus on the geometric properties of analytic functions
Geometric function theory was evolved around the turn of the 20th century and developed deep connections with other elds of mathematics and physics like hyperbolic geometry, theory of partial dierential equations, uid dynamics etc
Summary
Geometric function theory is one of the most important branches of complex analysis which focus on the geometric properties of analytic functions. Al-Shaqsi and Darus [1] dened the subclasses S∗(μ; φ), K(μ; φ), C(μ, η; φ, ψ) and C∗(μ, η; φ, ψ) of the class A in terms of the subordination principle between certain analytic functions. These subclasses are as follows: S∗(μ; φ) = f ∈ A : 1 zf (z) − μ ≺ φ(z). We dene certain k-integral operators and we introduce four subclasses Sβα,k(μ; φ), Kβα,k(μ; φ), Cβα,k(μ, η; φ, ψ) and QCβα,k(μ, η; φ, ψ) of the class A. We deduce certain inclusion relations for the classes Sβα,k(μ; φ), Kβα,k(μ; φ), Cβα,k(μ, η; φ, ψ) and QCβα,k(μ, η; φ, ψ)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Advances in the Theory of Nonlinear Analysis and its Application
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
