233 citations · 1.3k across the 48 of their papers we have counts for
4 papers · 2 filters
Applications of a duality between generalized trigonometric and hyperbolic functions
Hiroki Miyakawa, Shingo Takeuchi
It is shown that generalized trigonometric functions and generalized hyperbolic functions can be transformed from each other. As an application of this transformation, a number of…
Lyapunov-type inequalities for a Sturm-Liouville problem of the one-dimensional -Laplacian
Shingo Takeuchi, Kohtaro Watanabe
This article considers the eigenvalue problem for the Sturm-Liouville problem including -Laplacian \begin{align*} \begin{cases} \left(\vert u'\vert^{p-2}u'\right)'+\left(λ+r(x)\…
Remarkable properties of the functions and related integrals
Houry Melkonian, Shingo Takeuchi
Different types of sinc integrals are investigated when the standard sine function is replaced by the generalised in two parameters. A striking generalisation of the i…
Redheffer-type inequalities for generalized trigonometric functions
Shimpei Ozawa, Shingo Takeuchi
Famous Redheffer's inequality is generalized to a class of anti-periodic functions. We apply the novel inequality to the generalized trigonometric functions and establish several R…