Inequalities for the generalized trigonometric functions with respect to weighted power mean

Abstract The generalized trigonometric functions occur as an eigenfunction of the Dirichlet problem for the one-dimensional <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>p</m:mi> </m:math> p -Laplacian. In this study, the authors investigate some weighted power mean inequalities for the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>p</m:mi> </m:math> p -generalized trigonometric functions with certain conditions on the parameters <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>p</m:mi> </m:math> p , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>λ</m:mi> </m:math> \lambda .