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Some new inequalities of Hermite-Hadamard type fors-convex functions with applications

100%
Khan M. A., Chu Y., Khan T. U., Khan J.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1414-1430
EN
In this paper, we present several new and generalized Hermite-Hadamard type inequalities for s-convex as well as s-concave functions via classical and Riemann-Liouville fractional integrals. As applications, we provide new error estimations for the trapezoidal formula.
2
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On some properties of Hamel bases and their applications to Marczewski measurable functions

84%
Dorais F., Filipów R., Natkaniec T.
Open Mathematics
|
2013
|
tom 11
|
nr 3
487-508
EN
We introduce new properties of Hamel bases. We show that it is consistent with ZFC that such Hamel bases exist. Under the assumption that there exists a Hamel basis with one of these properties we construct a discontinuous and additive function that is Marczewski measurable. Moreover, we show that such a function can additionally have the intermediate value property (and even be an extendable function). Finally, we examine sums and limits of such functions.
3
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Improved Heinz inequalities via the Jensen functional

84%
Krnić M., Pečarić J.
Open Mathematics
|
2013
|
tom 11
|
nr 9
1698-1710
EN
By virtue of convexity of Heinz means, in this paper we derive several refinements of Heinz norm inequalities with the help of the Jensen functional and its properties. In addition, we discuss another approach to Heinz operator means which is more convenient for obtaining the corresponding operator inequalities for positive invertible operators.
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