Abstract
Our aim in this paper is to introduce some idea about generalized relative Nevanlinna order (α,β) and generalized relative Nevanlinna type (α,β) of an analytic function with respect to another analytic function in the unit disc where α and β are continuous non-negative functions on (-∞,+∞). So we discuss about some growth properties relating to the composition of two analytic functions in the unit disc on the basis of generalized relative Nevanlinna order (α,β) and generalized relative Nevanlinna type (α,β) as compared to the growth of their corresponding left and right factors.
Highlights
A function g which is analytic in the unit disc U = {z : |z| < 1} is said to have finite Nevanlinna order [1] if there exists a number μ for which the Nevanlinna characteristic function Tg (r) of g satisfies Tg (r) < (1 − r)−μ for all r in 0 < r0 (μ) < r < 1 where Tg (r) is defined as
For the purpose of further applications, Biswas et al [2] have introduced the definitions of the generalized Nevanlinna order (α, β) and generalized Nevanlinna lower order (α, β) of an analytic function g in the unit disc U which are as follows: Definition 1
In order to refine the growth scale namely the generalized relative Nevanlinna order (α, β), we introduce the definitions of another growth indicators, called generalized relative Nevanlinna type (α, β) and generalized relative Nevanlinna lower type (α, β) respectively of an analytic function g with respect to entire function w in the unit disc U which are as follows: Definition 5
Summary
We can introduce the definitions of the generalized relative Nevanlinna order (α, β) and generalized relative Nevanlinna lower order (α, β) of an analytic function g with respect to another entire function w in the unit disc U which are as follows: Definition 2. The generalized relative Nevanlinna hyper order (α, β) denoted by ρ(α,β)[g]w and generalized relative Nevanlinna hyper lower order (α, β) denoted by λ(α,β)[g]w of an analytic function g with respect to entire function w in the unit disc U are defined as: α(log Tw−1 (Tg(r)) )
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: Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
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.
