The main objective of this paper is to establish several new lower and upper bounds for the functions $\sinh x/x$ $\cosh x$. Following simple approach, our results give refinements generalizations some known inequalities involving these functions.

In this paper, a new two-dimensional sine-cosine coupling chaos map(2D-SCCM) is proposed. The performance of the proposed chaotic system analysed by using trajectory distribution maps, Lyapunov exponents, sample entropy and sequence sensitivity, etc. results show that 2D-SCCM has better randomness ergodicity, as well wider hyperchaotic range than existing partial maps. To verify its application...