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A study on t-best approximation problems in Fuzzy N-Formed Linear Spaces

Jacob, Kavikumar and Khamis, Azme and Md Raji, Abd Wahid (2012) A study on t-best approximation problems in Fuzzy N-Formed Linear Spaces. Other thesis, Universiti Tun Hussein Onn Malaysia.

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Abstract

A proble'm in fundamental mathematics is to find an approximation to the functions which are given explicitly or implicitly by operator equations, from a set of functions of simple structure. It is well known that the Approximation Theory of functions can be divided into Best, Good and Possible Approximation. The theory of best approximation is mainly concerned with the questions of existence, uniqueness, characterizations, qualitative properties of the minimizing functions and the approximations errors minimize when the complexity order of the system is increased. The best approximation is playing a vital role in engineering problems. It considers the problem of approximation defined on a set taking values in an normed and n-normed space. To find an approximation of the exact value, it must know something about the problem element. Usually the information is imprecise; thus there exist much information corresponding to same problem element. Under such an interpretation it seems natural to consider the information as fuzzy, rather than crisp. This is the motivation of the thesis to develop the concept of best approximation, best coapproximation in the framework of fuzzy normed and fuzzy n-normed syaces. The objective of this thesis is a systematize study of t-best approximation, t-best simultaneous approximation and t-best (simultaneous) coapproximation problems in fuzzy normed and fuzzy n-normed spaces X with respect to continuous t-norm. This study is useful for the development of fuzzy functional analysis and fuzzy approximation theory in order to get the precise solutions.

Item Type: Thesis (Other)
Subjects: Q Science > QA Mathematics > QA297 Numerical analysis. Analysis
Depositing User: Normajihan Abd. Rahman
Date Deposited: 07 Dec 2012 02:08
Last Modified: 07 Dec 2012 02:08
URI: http://eprints.uthm.edu.my/id/eprint/2871
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