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3 results

3 - Some Calculus
from PART I - Measure And Integration
Martin Buntinas, Loyola University, Chicago
Book:

Classical and Discrete Functional Analysis with Measure Theory

Published online:

06 January 2022

Print publication:

20 January 2022, pp 118-135
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Summary

This Chapter covers optional Calculus topics such as the Fubini Theorem, Riemann Integration, the Fundamental Theorem of Calculus, Integration by Parts, Mean Value Theorem, and Absolute Continuity.

Generalized monotonicity in terms of differential inequalities
Part of
- Real functions
- General theory in ordinary differential equations
Mihály Bessenyei
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 149 / Issue 6 / December 2019

Published online by Cambridge University Press:

16 January 2019, pp. 1473-1479

Print publication:

December 2019
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The classical notions of monotonicity and convexity can be characterized via the nonnegativity of the first and the second derivative, respectively. These notions can be extended applying Chebyshev systems. The aim of this note is to characterize generalized monotonicity in terms of differential inequalities, yielding analogous results to the classical derivative tests. Applications in the fields of convexity and differential inequalities are also discussed.

Time-dependent Lipschitz attractors for non-semigroup evolution processes
Part of
Mihai Turinici
Journal:

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 38 / Issue 1 / February 1985

Published online by Cambridge University Press:

09 April 2009, pp. 103-117

Print publication:

February 1985
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A maximality principle on quasi-ordered pseudo-metric spaces is used to obtain a number of Lipschitz attraction results for non-semigroup evolution processes with respect to time-dependent families. As particular cases, a multivalued version of Dieudonné's means value theorem and the Kirk-Ray lipschitzianness test are derived.

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3 results

3 - Some Calculus

Summary

Generalized monotonicity in terms of differential inequalities

Time-dependent Lipschitz attractors for non-semigroup evolution processes