Barkat Ali Bhayo

Full length article: On generalized trigonometric functions with two parameters

The generalized p-trigonometric and (p,q)-trigonometric functions were introduced by P. Lindqvist and S. Takeuchi, respectively. We prove some inequalities and present a few conjectures for the (p,q)-functions.

On Mori's theorem for quasiconformal maps in the n-space

R. Fehlmann and M. Vuorinen proved in 1988 that Moris constant M(n, K) for K-quasiconformal maps of the unit ball in R n onto itself keeping the origin fixed satisfies M(n, K) ! 1 when K ! 1 . We give here an alternative proof of this fact, with a quantitative upper bound for the constant in terms of elementary functions. Our proof is based on a refinement of a method due to G.D. Anderson and M. K. Vamanamurthy. We also give an explicit version of the Schwarz lemma for quasiconformal self-maps of the unit disk. Some experimental results are provided to compare the various bounds for the Mori constant when n = 2 .

ON GENERALIZED COMPLETE ELLIPTIC INTEGRALS AND MODULAR FUNCTIONS

This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.