The Construction of Hilbert Spaces over the Non-Newtonian Field

Uğur Kadak and Hakan Efe

International Journal of Analysis, 2014, vol. 2014, 1-10

Abstract:

Although there are many excellent ways to present the principle of the classical calculus, the novel presentations probably lead most naturally to the development of the non-Newtonian calculi. In this paper we introduce vector spaces over real and complex non-Newtonian field with respect to the -calculus which is a branch of non-Newtonian calculus. Also we give the definitions of real and complex inner product spaces and study Hilbert spaces which are special type of normed space and complete inner product spaces in the sense of -calculus. Furthermore, as an example of Hilbert spaces, first we introduce the non-Cartesian plane which is a nonlinear model for plane Euclidean geometry. Secondly, we give Euclidean, unitary, and sequence spaces via corresponding norms which are induced by an inner product. Finally, by using the -norm properties of complex structures, we examine Cauchy-Schwarz and triangle inequalities.

Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/ANALYSIS/2014/746059.pdf (application/pdf)
http://downloads.hindawi.com/journals/ANALYSIS/2014/746059.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:ijanal:746059

DOI: 10.1155/2014/746059

Access Statistics for this article

More articles in International Journal of Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().