Abstract
AbstractBased on iteration of random-valued functions we study the problem of solvability in the class of continuous and Hölder continuous functions $$\varphi $$
φ
of the equations $$\begin{aligned} \varphi (x)=F(x)-\int _{\Omega }\varphi \big (f(x,\omega )\big )P(d\omega ),\\ \varphi (x)=F(x)+\int _{\Omega }\varphi \big (f(x,\omega )\big )P(d\omega ), \end{aligned}$$
φ
(
x
)
=
F
(
x
)
-
∫
Ω
φ
(
f
(
x
,
ω
)
)
P
(
d
ω
)
,
φ
(
x
)
=
F
(
x
)
+
∫
Ω
φ
(
f
(
x
,
ω
)
)
P
(
d
ω
)
,
where P is a probability measure on a $$\sigma $$
σ
-algebra of subsets of $$\Omega $$
Ω
.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,General Mathematics
Reference13 articles.
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2. Baron, K.: On the convergence in law of iterates of random-valued functions. Aust. J. Math. Anal. Appl. 6, no. 1, Art. 3 (2009)
3. Baron, K.: Weak limit of iterates of some random–valued functions and its application. Aequ. Math. 94, 415–425; 427 (Correction) (2020)
4. Baron, K.: Around the weak limit of iterates of some random-valued functions. Ann. Univ. Budapest. Sect. Comput. 51, 31–37 (2020)
5. Baron, K., Kapica, R., Morawiec, J.: On Lipschitzian solutions to an inhomogeneous linear iterative equation. Aequ. Math. 90, 77–85 (2016)
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