Some new bounds for ratio functions of trigonometric and hyperbolic functions

proved a Sturm bound for certain general automorphic cusp forms on GL 2 over K: for harmonic cochains, one can derive bounds of the form 5 deg n + 5 for normalized Hecke

Bagul, New inequalities involving circular, inverse circu- lar, hyperbolic, inverse hyperbolic and exponential functions, Ad- vances in Inequalities and Applications, Volume

Using the developed general technique, we derive uniform bounds on the L s -norms of empirical and regression-type processes.. Use- fulness of the obtained results is illustrated

For deriving such bounds, we use well known results on stochastic majorization of Markov chains and the Rogers-Pitman’s lumpability criterion.. The proposed method of comparison

Neuman, Refinements and generalizations of certain inequalities involving trigono- metric and hyperbolic functions, Advances in Inequalities and Applications, Vol. Qi, A

Then we propose two improvements of this lower bound by using two different approaches; the first approach consists in adding well-chosen polynomial term to it, whereas the

We provide alternative proofs to existing results on exponential bounds, with some improvements, by using infinite products and the so- called Bernoulli inequality..

We aim to obtain very tight exponential bounds for hyperbolic tangent by first establishing simple algebraic bounds for this function.. Our inequalities refine a double inequality