Zeros of Analytic Functions with Restricted Coefficients

P. Ramulu¹ , G.L. Reddy²

1. Department of Mathematics, M.V.S. Govt. Arts & Science College (Autonomous), Mahabubnagar509001, Telangana, India.
2. School of Mathematics and Statistics, University of Hyderabad-500046, Telangana, India.

Correspondence should be addressed to: ramulu.purra@gmail.com.

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.2 , pp.146-151, Apr-2020

Online published on Apr 30, 2020

Copyright © P. Ramulu, G.L. Reddy . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, we consider the problem of finding the number of zeros of a special class of analytic functions of polynomial functions in prescribed regions, by subjecting the certain restrictions on the real and imaginary coefficient for a certain stage by taking even and odd cases in our results. Our results generalized the earlier known results with the hypothesis about some special restriction on the real part and monotonic on imaginary parts of the polynomial coefficients and improved many theorems and corollaries. We have been working with the Eneström-Kakeya theorem hypothesis by about the number of zeros of a polynomial with restrictions. As special cases, the extended results yield much simpler expressions for the upper bounds of zeros of those existing results with the different types of restrictions on the coefficients of a polynomial and improved the many theorems and corollaries by taking analytic functions with complex coefficient.

Key-Words / Index Term :
Zeros of polynomial, Analytic functions, Eneström-Kakeya theorem, Number of Zeros, Regions

References :
[1]. G.Eneström, Remarquee sur un théorème relatif aux racines de l’equation a_n+...+a_0=0 oütous les coefficient sont et positifs, Tôhoku Math.J 18(1920),34-36.
[2]. S.KAKEYA, On the limits of the roots of an alegebraic equation with positive coefficient, Tôhoku Math.J 2 (1912-1913),140-142.
[3]. A. Aziz and Q.G. Mahammad, on the certain class of analytic class of olynomial and related analytic functions, J. Anal and Appl. 75,[1980], 495-502.
[4]. N.K.Govil and Q.I.Rehman, On the EnstromKakeya Theorem Tohoku Math .J. 20, (1968), 126-136.
[5]. K. K. Dewan, Extremal Properties and Coefficient Estimates for Polynomials with Restricted Zeros and on Location of Zeros of Polynomials, Ph.D Thesis, Indian Institutes of Technology, Delhi, 1980.
[6]. P.Ramulu, G.L.Reddy, On the zeros of polynomials, Int Jr. of Mathematical Sciences & Applications, Vol. 5, No. 2, (July-December, 2015), pp-395-399.
[7]. P. Ramulu, Some Generalization of Eneström-Kakeya Theorem: International Journal of Mathematics and Statistics Invention IJMSI), (2015), 3 (2), 52-59.
[8]. P. Ramulu, G. L. Reddy and C.Gangadhar on the zeros of polynomials with real coefficients: International Journal of Applied Mathematical Sciences. (2015), 5 (2), 109-118.
[9]. G.L.Reddy, and P. Ramulu On the zeros of Polynomials: International Journal Mathematical Sciences and Applications, (2015), 5 (2), 395-399.