SINGULAR VALUES AND REAL FIXED POINTS OF ONE-PARAMETER FAMILIES ASSOCIATED WITH FUNDAMENTAL TRIGONOMETRIC FUNCTIONS\\[4pt] $\sin z$, $\cos z$ and $\tan z$

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 fμ(z) = sin z z+μ , gη(z) = cos z z+η and hκ(z) = tan z z2 + κ for μ > 0, η > 0 and κ > 0 respectively, and z ∈ C. It is found that the functions fμ(z) and gη(z) have infinite number of bounded singular values while the function hκ(z) has infinite number of unbounded singular values. Moreover, the real fixed points of fμ(z), gη(z) and hκ(z) are described. AMS Subject Classification: 30D05; 37C25; 58K05