23,972 research outputs found
Some sharp inequalities involving Seiffert and other means and their concise proofs
In the paper, by establishing the monotonicity of some functions involving
the sine and cosine functions, the authors provide concise proofs of some known
inequalities and find some new sharp inequalities involving the Seiffert,
contra-harmonic, centroidal, arithmetic, geometric, harmonic, and root-square
means of two positive real numbers and with .Comment: 10 page
Geometric convexity of the generalized sine and the generalized hyperbolic sine
In the paper, the authors prove that the generalized sine function
and the generalized hyperbolic sine function
are geometrically concave and geometrically convex, respectively. Consequently,
the authors verify a conjecture posed in the paper "B. A. Bhayo and M.
Vuorinen, On generalized trigonometric functions with two parameters, J.
Approx. Theory 164 (2012), no.~10, 1415\nobreakdash--1426; Available online at
\url{http://dx.doi.org/10.1016/j.jat.2012.06.003}".Comment: 5 page
Solution of the Dirichlet Problem for Degenerate -Hessian Equations
In this paper, we prove the existence of -solution to the Dirichlet
problem for degenerate elliptic -Hessian equations under a
condition which is weaker than the condition .Comment: 18page
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