Abstract
AbstractIn this paper, two new estimators $$ E_{2^{k-1},0}^{(1)}(f) $$
E
2
k
-
1
,
0
(
1
)
(
f
)
and $$ E_{2^{k-1},M}^{(1)}(f) $$
E
2
k
-
1
,
M
(
1
)
(
f
)
of characteristic function and an estimator $$ E_{2^{k-1},M}^{(2)}(f) $$
E
2
k
-
1
,
M
(
2
)
(
f
)
of function of H$$\ddot{\text {o}}$$
o
¨
lder’s class $$H^{\alpha } [0,1)$$
H
α
[
0
,
1
)
of order $$0<\alpha \leqslant 1$$
0
<
α
⩽
1
have been established using Bernoulli wavelets. A new technique has been applied for solving Volterra integral equation of second kind using Bernoulli wavelet operational matrix of integration as well as product operational matrix. These matrices have been utilized to reduce the Volterra integral equation into a system of algebraic equations, which are easily solvable. Some examples are illustrated to show the validity and efficiency of proposed technique of this research paper.
Publisher
Springer Science and Business Media LLC
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