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The purpose of this corrigendum is to correct an error in the earlier paper by the authors: Generalizations of Opial-type inequalities in several independent variables, Demonstratio Math.
The aim of this paper is to give an extension of an inequality proved by Wulbert (Math Comput Model 37:1383–1391, 2003, Lemma 2.5) and to define Stolarsky type means as an application of this inequality. Further, we discuss some properties of averages of a continuous convex function, some consequences of a double inequality given by Wulbert (Math C...
Let -infinity < a < b < infinity. If f is concave on [a, b] and psi ' is convex on the interval of integration, then Wulbert proved that 1/delta(+) - delta(-) integral(delta+)(delta-) psi(u)du >= 1/b - a integral(b)(a) psi(f(x))dx, where delta(-) = (f) over bar - root 3(parallel to f parallel to(2)(2) - ((f) over bar)(2))(1/2), delta(+) = (f) over...
The object is to give an overview of the study of Schur-convexity of various means and functions and to contribute to the subject with some new results. First, Schur-convexity of the generalized integral and weighted integral quasiarithmetic mean is studied. Relation to some already published results is established, and some applications of the ext...
We generalize means of Stolarsky type and show the monotonicity of these generalized means.
Using D. E. Wulbert’s result from [Math. Comput. Modelling 37, No. 12–13, 1383–1391 (2003; Zbl 1081.90051)], we deduce a method for constructing exponentially convex functions. To this date there is no known operative criteria for recognizing exponentially convex functions, so our method is of a special interest since there is a lack of examples of...