Abstract
AbstractIn this paper, we study a functional equation for generating functions of the form $$f(z) = g(z) \sum _{i=1}^M p_i f(\alpha _i(z)) + K(z)$$
f
(
z
)
=
g
(
z
)
∑
i
=
1
M
p
i
f
(
α
i
(
z
)
)
+
K
(
z
)
, viz. a recursion with multiple recursive terms. We derive and analyze the solution of this equation for the case that the $$\alpha _i(z)$$
α
i
(
z
)
are commutative contraction mappings. The results are applied to a wide range of queueing, autoregressive and branching processes.
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,Management Science and Operations Research,Computer Science Applications
Cited by
3 articles.
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