Some inequalities for the generalized sine and the generalized hyperbolic sine

Geometric Convexity of the Generalized Sine and the Generalized Hyperbolic Sine

In the paper, the authors prove that the generalized sine function sinp,q(x) and the generalized hyperbolic sine function sinhp,q(x) 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–...

Generalized solution of Sine-Gordon equation

In this paper, we are interested to study the Sine-Gordon equation in generalized functions theory introduced by Colombeau, in the first we give result of existence and uniqueness of generalized solution with initial data are distributions (elements of the Colombeau algebra). Then we study the association concept with the classical solution.

Some Generalized Trigonometric Sine Functions and Their Applications

In this paper, it is shown that D. Shelupsky’s generalized sine function, and various general sine functions developed by P. Drábek, R. Manásevich and M. Ôtani, P. Lindqvist, including the generalized Jacobi elliptic sine function of S. Takeuchi can be defined by systems of first order nonlinear ordinary differential equations with initial conditions. The structure of the system of differential...

generalized solution of sine-gordon equation

in this paper, we are interested to study the sine-gordon equation in generalized functions theory introduced by colombeau, in the first we give result of existence and uniqueness of generalized solution with initial data are distributions (elements of the colombeau algebra). then we study the association concept with the classical solution.

New Inequalities of Shafer-Fink Type for Arc Hyperbolic Sine