Fuzzy Mathematics: Approximation Theory
George A. Anastassiou
This monograph belongs to the broader area of Fuzzy Mathematics and it is the first one in Fuzzy
Approximation Theory. Chapters are self

contained with lots of applications and several
advanced
courses
can be taught.
The topics covered are ver
y
diverse. An extensive
background of
Fuzziness and
F
uzzy Real Analysis is given.
The author
cover
s
Fuzzy Differentiati
on and Integration Theory. It follows
about
Fuzzy Ostrowski
i
ne
qualities.
Then are
present
ed
results on classical algebraic and trigonometric
polynomial Fuzzy Ap
proximation. The author
develop
s a complete
theory of convergence with rates of
Fuzzy Positive linear
operators to Fuzzy u
nit operator, the so called Fuzzy Kor
ovkin Th
eory.The related
Fuzzy
Global Smoothness is included. Then follows the study of
Fuzzy Wavelet type operators and their
c
onvergence with rates to Fuzzy u
nit operator
. Similarly are discussed
the Fuzzy Neural Network
Opera
tors. It follows about Fuzzy Rando
m Korovkin
approximation th
eory and
Fuzzy Random Neural
Network approximations.
The author continues with Fuzzy Korovkin approximations in the s
ense of
Summability.
At last are
estimate
d
in the fuzzy sense differences of Fuzzy Wavelet type operators.
The monograph's approach
is quantitative and the
main resul
ts are given via
Fuzzy inequalities,
involving F
uzzy
moduli of continuity, that is F
uzzy Jackson type
inequalities.
The exposed theory is destined and expected to find applications to all aspe
cts of Fuzziness from
theoretical to practical in almost all sciences, technology
, finance
and ind
ustry. Also it has its
interest
with
in
Pure Mathematics. So this monograph is suitable for researchers, graduate students and
seminars of theoretical and appl
ied mathematics, computer science,
statistics and
e
ngineering.
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