A study on t-best approximation problems in Fuzzy N-Formed Linear Spaces
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...
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| Main Authors: | , , |
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| Format: | Thesis |
| Published: |
2012
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| Subjects: | |
| Online Access: | http://eprints.uthm.edu.my/2871/ http://eprints.uthm.edu.my/2871/1/FRGS_0555.pdf |
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| Summary: | 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. |
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