Linear functional equations and their solutions in generalized Orlicz spaces
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AbstractAssume that $$\Omega \subset \mathbb {R}^k$$ Ω ⊂ R k is an open set, V is a real separable Banach space and $$f_1,\ldots ,f_N :\Omega \rightarrow \Omega $$ f 1 , … , f N : Ω → Ω , $$g_1,\ldots , g_N:\Omega \rightarrow \mathbb {R}$$ g 1 , … , g N : Ω → R , $$h_0:\Omega \rightarrow V$$ h 0 : Ω → V are given functions. We are interested in the existence and uniqueness of solutions $$\varphi :\Omega \rightarrow V$$ φ : Ω → V of the linear equation $$\varphi =\sum _{k=1}^{N}g_k\cdot (\varphi \circ f_k)+h_0$$ φ = ∑ k = 1 N g k · ( φ ∘ f k ) + h 0 in generalized Orlicz spaces.
Existence and uniqueness of solutions in H1(Δ) of a general class of non-linear functional equations
2003 ◽
Vol 279
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pp. 451-462
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2004 ◽
Vol 295
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pp. 287-289
1974 ◽
Vol 29
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pp. 89-118
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1975 ◽
Vol 31
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pp. 145-157
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1965 ◽
Vol 17
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pp. 367-372
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