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Constructions of contents and measures satisfying a prescribed set of integral inequalities

100%

Hoffmann-Jørgensen J.

Probability and Mathematical Statistics

2006

tom Vol. 26, Fasc. 2

283--313

Let ɸ be a given set of real-valued functions on the set T and let ß: ɸ → R given functional with values in the extended real line R = [−∞, ∞]. The objective of the paper is to construct contents or measures μ with good regularity and smoothness properties satisfying the integral inequalities ∫* φ dμ ≤ ß (φ), where ∫* denotes the upper integral.

Oscillation criteria for second-order functional difference equation with neutral terms

88%

Bolat Y.

2008

tom Vol. 41, nr 3

615-625

In this manuscript, two type of new oscillation criteria are obtained respect to coefficient ak in the following Eq. (1.1). In the subsection 2.1 considered as ak > 0. In the subsection 2.2 allowed it to be an oscillating sequence. There are no results for the oscillation of second order difference equations with oscillating coefficients up to now.