Complementary inequalities involving the Stolarsky mean.
Construction of aggregation operators: new composition method
A new construction method for aggregation operators based on a composition of aggregation operators is proposed. Several general properties of this construction method are recalled. Further, several special cases are discussed. It is also shown, that this construction generalizes a recently introduced twofold integral, which is exactly a composition of the Choquet and Sugeno integral by means of a min operator.
Continuously differentiable means.
Convex functions with respect to logarithmic mean and ѕandwich theorem
Convex sets and inequalities.
Convexity of the zero-balanced Gaussian hypergeometric functions with respect to Hölder means.
Cyclic mean-value inequalities for the gamma function
Differences of weighted mixed symmetric means and related results.
Distribution of terms of a logarithmic sequence.
Extending means of two variables to several variables.
Fixed points and iterations of mean-type mappings
Let (X, d) be a metric space and T: X → X a continuous map. If the sequence (T n)n∈ℕ of iterates of T is pointwise convergent in X, then for any x ∈ X, the limit is a fixed point of T. The problem of determining the form of µT leads to the invariance equation µT ○ T = µT, which is difficult to solve in general if the set of fixed points of T is not a singleton. We consider this problem assuming that X = I p, where I is a real interval, p ≥ 2 a fixed positive integer and T is the mean-type mapping...
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...
Improvement of an Ostrowski type inequality for monotonic mappings and its application for some special means.
Inequalities for general integral means.
Inequalities for generalized logarithmic means.
Inequalities for weighted power pseudo means.