Selected Topics On Generalized Integration
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Banach Spaces
Category=PBKB
Category=PBKF
Distribution Theory
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Functional Analysis
Gauge Integration
Generalized Integration Theory
Harmonic Analysis
Henstock-Kurzweil Integral
HenstockAcAEURA"Kurzweil Integral
McShane Integral
Measure Theory
Metric Measure Spaces
Mittag-Leffler Functions
Non-absolute Integration
q-Homotopy Analysis Method
Radon-Nikodym Theorem
Real Analysis
Riemann-type Integrals
Set-valued Integrals
Sugeno Integral
Symmetric Laplace Integral
Variational Integration
Vector-valued Integration
Product details
- ISBN 9789819812196
- Publication Date: 20 Jun 2025
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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This comprehensive volume offers an in-depth exploration of advanced integration theories, extending beyond classical methods to unify and expand the field. Building on the foundational work of Jaroslav Kurzweil and Ralph Henstock, the book delves into the Henstock-Kurzweil and McShane gauge integrals, presenting a more intuitive and versatile alternative to the traditional Lebesgue integral. By bridging gaps in existing literature, the authors provide a rigorous treatment of integration on metric measure spaces, exploring critical concepts such as completeness, compactness, and Cousin's lemma.The book systematically introduces advanced topics, including the variational Henstock integral in locally convex spaces, the Riemann-Lebesgue integral for vector-valued functions, and generalizations of the Sugeno integral. Further chapters explore convergence in Banach spaces on time scales, set-valued integrals, and applications to harmonic analysis and partial differential equations, including solutions to the heat equation in distribution spaces.Notably, the text presents innovative approaches like the symmetric Laplace integral and the q-Homotopy Analysis Method for solving nonlinear integral equations, offering practical tools for modern analysis. Unified integral representations for generalized Mittag-Leffler functions further highlight the book's engagement with special functions.Ideal for researchers and advanced students in mathematical analysis, this book seamlessly integrates classical theories with modern advancements, offering both theoretical insights and practical applications across mathematics, physics, and engineering.
