SINGULAR VALUES AND REAL FIXED POINTS OF
ONE-PARAMETER FAMILIES ASSOCIATED WITH
FUNDAMENTAL TRIGONOMETRIC FUNCTIONS sin z, cos z and tan z
Mohammad Sajid
Mechanical Engineering Department
College of Engineering, Qassim University
Buraidah-51452, Al Qassim, SAUDI ARABIA

Abstract

This article is devoted to investigate the singular values as well as the real fixed points of one-parameter families of transcendental meromorphic functions which are associated with fundamental trigonometric functions $\sin z$, $\cos z$ and $\tan z$. For this purpose, we consider the functions $f_{\mu}(z)={\frac{\sin z}{z^{2}+\mu}}$, $g_{\eta}(z)={\frac{\cos z}{z^{2}+\eta}}$ and $h_{\kappa}(z)=\dfrac{\tan z}{z^{2}+\kappa}$ for $\mu >0$, $\eta>0$ and $\kappa>0$ respectively, and $z \in {\mathbb{C}}$. It is found that the functions $f_{\mu}(z)$ and $g_{\eta}(z)$ have infinite number of bounded singular values while the function $h_{\kappa}(z)$ has infinite number of unbounded singular values. Moreover, the real fixed points of $f_{\mu}(z)$, $g_{\eta}(z)$ and $h_{\kappa}(z)$ are described.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 4
Year: 2020

DOI: 10.12732/ijam.v33i4.8

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