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LIP C r <a, b> SOLUTIONS OF A LINEAR FUNCTIONAL EQUATION

LIP C r SOLUTIONS OF A LINEAR FUNCTIONAL EQUATION DEMONSTRATIO MATHEMATICAV o l . XIXNo 21986Jadwiga J e l o n e kLIP CT&lt;a, b&gt; SOLUTIONS OF A LINEAR FUNCTIONAL EQUATIONLet Ac A1 be a compact and l e t Lip C^fA), r e N t denote thea e t of a l l f u n c t i o n s r - t i m e s d i f f e r e n t i a t e (p : A —- R suoht h a t r - t h d e r i v a t i v e f u l f i l s the L i p s o h i t z c o n d i t i o n i n A.For 9 e Lip (^(A) we w r i t eU^1^):=supx,xt Ax^x,i=0,1,...,r,9&gt;{o)I t i s w e l l known t h a t Lip (^(A) w i t h the normr(1)&lt;p{i)lV||9&gt;|| :=| +U&lt;P{V))i=0i s a Banaoh s p a o e . I n t h i s f o r m u l a | e A i s a r b i t r a r i l y f i http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

LIP C r <a, b> SOLUTIONS OF A LINEAR FUNCTIONAL EQUATION

Jelonek, Jadwiga
Demonstratio Mathematica , Volume 19 (2): 12 – Apr 1, 1986
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References (2)

Publisher
de Gruyter
Copyright
© by Jadwiga Jelonek
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1986-0202
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAV o l . XIXNo 21986Jadwiga J e l o n e kLIP CT&lt;a, b&gt; SOLUTIONS OF A LINEAR FUNCTIONAL EQUATIONLet Ac A1 be a compact and l e t Lip C^fA), r e N t denote thea e t of a l l f u n c t i o n s r - t i m e s d i f f e r e n t i a t e (p : A —- R suoht h a t r - t h d e r i v a t i v e f u l f i l s the L i p s o h i t z c o n d i t i o n i n A.For 9 e Lip (^(A) we w r i t eU^1^):=supx,xt Ax^x,i=0,1,...,r,9&gt;{o)I t i s w e l l known t h a t Lip (^(A) w i t h the normr(1)&lt;p{i)lV||9&gt;|| :=| +U&lt;P{V))i=0i s a Banaoh s p a o e . I n t h i s f o r m u l a | e A i s a r b i t r a r i l y f i

Journal

Demonstratio Mathematica – de Gruyter

Published: Apr 1, 1986

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