By Gerald Edgar
By V. Vasil'ev
By Gaston M. N'Guérékata
By Yeol Je Cho,Yu-Qing Chen
The authors start via introducing the Brouwer measure thought in Rn, then examine the Leray-Schauder measure for compact mappings in normed areas. subsequent, they discover the measure conception for condensing mappings, together with functions to ODEs in Banach areas. this can be via a research of measure concept for A-proper mappings and its purposes to semilinear operator equations with Fredholm mappings and periodic boundary price difficulties. the point of interest then turns to development of Mawhin's twist of fate measure for L-compact mappings, through a presentation of a level concept for mappings of sophistication (S+) and its perturbations with different monotone-type mappings. the ultimate bankruptcy experiences the fastened aspect index thought in a cone of a Banach house and provides a outstanding new mounted aspect index for countably condensing maps.
Examples and routines supplement every one bankruptcy. With its mix of outdated and new concepts, Topological measure concept and functions types a very good textual content for self-study or specific subject matters classes and a invaluable reference for a person operating in differential equations, research, or topology.
By Silvio Ghilardi,M. Zawadowski
By Carlo Viola
The matters handled during this ebook were specially selected to symbolize a bridge connecting the content material of a primary path at the trouble-free idea of analytic capabilities with a rigorous therapy of a few of an important specific services: the Euler gamma functionality, the Gauss hypergeometric functionality, and the Kummer confluent hypergeometric functionality. Such unique capabilities are imperative instruments in "higher calculus" and are often encountered in just about all branches of natural and utilized arithmetic. the one wisdom assumed at the a part of the reader is an realizing of uncomplicated techniques to the extent of an straight forward path protecting the residue theorem, Cauchy's quintessential formulation, the Taylor and Laurent sequence expansions, poles and crucial singularities, department issues, etc. The e-book addresses the wishes of complex undergraduate and graduate scholars in arithmetic or physics.
By Hans Wilhelm Alt,Robert Nürnberg
By Alexander Kharazishvili
Strange services in actual research explores a few very important examples and buildings of pathological capabilities. After introducing the elemental suggestions, the writer starts off with Cantor and Peano-type services, then strikes to services whose structures require basically noneffective tools. those comprise capabilities with no the Baire estate, capabilities linked to a Hamel foundation of the true line, and Sierpinski-Zygmund services which are discontinuous on each one subset of the genuine line having the cardinality continuum. eventually, he considers examples of capabilities whose life can't be tested with no assistance from extra set-theoretical axioms and demonstrates that their lifestyles follows from sure set-theoretical hypotheses, comparable to the Continuum Hypothesis.
By Mohamed Tarek Hussein Mohamed Ouda
By Hemen Dutta,Billy E. Rhoades
This ebook discusses contemporary advancements in and modern learn on summability thought, together with normal summability equipment, direct theorems on summability, absolute and powerful summability, precise equipment of summability, useful analytic tools in summability, and comparable themes and purposes. All contributing authors are eminent scientists, researchers and students of their respective fields, and hail from worldwide. The booklet can be utilized as a textbook for graduate and senior undergraduate scholars, and as a beneficial reference advisor for researchers and practitioners within the fields of summability idea and practical analysis.
Summability idea is usually utilized in research and utilized arithmetic. It performs a big half within the engineering sciences, and numerous elements of the speculation have lengthy seeing that been studied by means of researchers all around the world.