On Parabolic Analytic Functions with Respect to Symmetrical Points

Authors

Khalida Inayat Noor, Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan.Follow
Humayoun Shahid, Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan.Follow
Muhammad Aslam Noor, Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan.Follow

Author Country (or Countries)

Pakistan.

Abstract

Let A be the class of functions f , f(z) = z + ∞ ∑ m=2 amz m, analytic in the open unit disc E. Let S ∗ s (h) consist of functions f ∈ A such that 2z f′ (z) f(z)−f(−z) ≺ h(z), where ≺ denotes subordination and h(z) is analytic in E with h(0) = 1. For n = 0,1,2,3,..., a certain integral operator In : A → A is defined as In f = f −1 n ∗ f such that (f −1 n ∗ fn)(z) = z z−1 , where fn(z) = z (1−z) n+1 , and ∗ denotes convolution. By taking h(z) = 1+ 2 π 2 log 1+ √ z 1− √ z 2 α ,0 < α < 1, and using the operator In, we define some new classes USTs(n,α) and UKs(n,α), and study some interesting properties of these classes. The ideas and techniques of this paper may motivate further research in this field

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100135

Recommended Citation

Inayat Noor, Khalida; Shahid, Humayoun; and Aslam Noor, Muhammad (2016) "On Parabolic Analytic Functions with Respect to Symmetrical Points," Applied Mathematics & Information Sciences: Vol. 10: Iss. 1, Article 35.
DOI: http://dx.doi.org/10.18576/amis/100135
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss1/35