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

Bolat Y.

Demonstratio Mathematica

2008

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.

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

Hoffmann-Jørgensen J.

Probability and Mathematical Statistics

2006

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.