Generalization of integral inequalities for functions whose modulus of derivatives are convex.
Generalization of Stolarsky type means.
Generalizations of a class of inequalities for products.
Generalized abstracted mean values.
Generalized weighted quasi-arithmetic means and the Kolmogorov-Nagumo theorem
A generalization of the weighted quasi-arithmetic mean generated by continuous and increasing (decreasing) functions , k ≥ 2, denoted by , is considered. Some properties of , including “associativity” assumed in the Kolmogorov-Nagumo theorem, are shown. Convex and affine functions involving this type of means are considered. Invariance of a quasi-arithmetic mean with respect to a special mean-type mapping built of generalized means is applied in solving a functional equation. For a sequence of...