Search

In the paper, the authors find and apply necessary and sufficient conditions for a bivariate mean of two positive numbers with three parameters to be Schur convex or Schur harmonically convex respectively.

In this paper, the authors propose the notions of (α,s)-geometric-arithmetically convex functions and (α,s,m)-geometric-arithmetically convex functions, while they establish some new integral inequalities of the Hermite–Hadamard type for (α,s)-geometric-arithmetically convex functions and for (α,s,m)-geometric-arithmetically convex functions.

In the paper, with the help of two known integral identities and by virtue of the classical Hölder integral inequality, the authors establish several new integral inequalities of the Hermite–Hadamard type for convex functions. These newly established inequalities generalize some known results.