Basis properties of generalized trigonometric functions

Generalized Trigonometric Functions: 10744

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Inequalities involving generalized trigonometric and hyperbolic functions

The Huygens-Wilker type inequalities involving generalized trigonometric functions and generalized hyperbolic functions are established. The first and the second inequalities of Huygens and Wilker, for classes of functions under discussion, are also investigated.

DIFFERENTIABILITY PROPERTIES OF p-TRIGONOMETRIC FUNCTIONS

p-trigonometric functions are generalizations of the trigonometric functions. They appear in context of nonlinear differential equations and also in analytical geometry of the p-circle in the plain. The most important ptrigonometric function is sinp(x). For p > 1, this function is defined as the unique solution of the initial-value problem (|u′(x)|p−2u′(x))′ = (p− 1)|u(x)|p−2u(x), u(0) = 0, u′(...

Stability of Trigonometric Functional Equations in Generalized Functions

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...