Affiliation:
1. Department of Mathematics, College of Science and Arts, Al-Badaya, Qassim University, Buraidah 52571, Saudi Arabia
2. Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
3. Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Abstract
In this paper, we define three subclasses Mp,αn,q(η,A,B),Ip,αn(λ,μ,γ),, Rpn,q(λ,μ,γ) connected with a q-analogue of linear differential operator Dα,p,Gn,q which consist of functions F of the form F(ζ)=ζ−p+∑j=1−p∞ajζj(p∈N) satisfying the subordination condition p−1ηζDα,p,Gn,qF(ζ)′Dα,p,Gn,qF(ζ)+p≺p1+Aζ1+Bζ.Also, we study the various properties and characteristics of this subclass Mp,αn,q,∗(η,A,B) such as coefficients estimate, distortion bounds and convex family. Also the concept of δneighborhoods and partial sums of analytic functions to the class Mp,αn,q(η,A,B).
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
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