SOME RESULTS ON VALUE DISTRIBUTION THEORY FOR E-VALUED MEROMORPHIC FUNCTION


By

Ashok Rathod1 and Shreekant Patil2

1Department of Mathematics, KLE Society’s G I Bagewadi Arts Science and Commerce College, Nippani-591237, Karnataka, India

2Department of Mathematics, BLDEA’s S.B. Arts and K.C.P. Science College, Vijayapur-586103, Karnataka, India

Email:ashokmrmaths@gmail.com, shreekantpatil949@gmail.com

(Received : October 22, 2021; Revised : November 13, 2021 ; Accepted : June 06,2022)


Abstract

In this paper, we investigate analogous of Milloux inequality and Hayman’s alternative for E-valued meromorphic functions from the complex plane ℂ to an infinite dimensional complex Banach space E with a Schauder basis. As an application of our results, we deduce some interesting analogous results for E-valued meromorphic functions from the complex plane ℂ to an infinite dimensional complex Banach space E with a Schauder basis. And also we have given the applications of homogeneous differential polynomials to the Nevanlinna’s theory of E-valued meromorphic functions from the complex plane ℂ to an infinite dimensional complex Banach space E with a Schauder basis and given some generalizations by these polynomials.


2020 Mathematical Sciences Classification: 34M10, 30D35.

Keywords and Phrases: Nevanlinna theory; meromorphic function; an infinite dimensional complex Banach space



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