Browsing by Author "Witkowski, Alfred"

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Access status: Open Access ,
Corrigendum to »Hermite-Hadamard type inequalities for Wright-convex functions of several variables« [Opuscula Math. 35, no. 3 (2015), 411-419]
(2016) Witkowski, Alfred
We correct a small mistake made by the authors of the paper [<a href="https://repo.agh.edu.pl/handle/AGH/50355"><i>Hermite-Hadamard type inequalities for Wright-convex functions of several variables</i></a>, Opuscula Math. 35, no. 3 (2015), 411-419].
Access status: Open Access ,
Generalized Levinson’s inequality and exponential convexity
(2015) Pečarić, Josip E.; Praljak, Marjan; Witkowski, Alfred
We give a probabilistic version of Levinson’s inequality under Mercer’s assumption of equal variances for the family of 3-convex functions at a point. We also show that this is the largest family of continuous functions for which the inequality holds. New families of exponentially convex functions and related results are derived from the obtained inequality.
Access status: Open Access ,
On some inequality of Hermite-Hadamard type
(2012) Wąsowicz, Szymon; Witkowski, Alfred
It is well-known that the left term of the classical Hermite–Hadamard inequality is closer to the integral mean value than the right one. We show that in the multivariate case it is not true. Moreover, we introduce some related inequality comparing the methods of the approximate integration, which is optimal. We also present its counterpart of Fejér type.