Abstract
This chapter presents some abstract concepts and definitions. A fundamental concept is that of a function as a thing in it. The usefulness of quasi-geometric approach, which is that of functional analysis, lies mainly in establishing general theorems from which many diverse results may be deduced as special cases. If F is a set of functions defined over a domain X, the set F is a linear vector space, or simply a vector space, over the field of real numbers if it is closed under addition and multiplication. The set of all functions on X is a vector space, but in practice one normally considers some closed subspace of this. An important example of a seminorm is the modulus of continuity. When a function is not known to be differentiable, the modulus of continuity gives a convenient measure of its smoothness.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
