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BC-SOLUTIONS OF NONLINEAR FUNCTIONAL EQUATION—A NONUNIQUENESS CASE

BC-SOLUTIONS OF NONLINEAR FUNCTIONAL EQUATION—A NONUNIQUENESS CASE DEMONSTRATIO MATHEMATICAVol. XXVINo 21993Tadeusz KostrzewskiJ9C-SOLUTIONS OF N O N L I N E A R F U N C T I O N A LEQUATION—A NONUNIQUENESS CASE1. S o m e properties of B C [ a , b] spaceBy B C [ a , 6] we denote the linear space of all functions <p : [a, 6] —• R ofthe form <p = t p i — i p 2 , where i p 1,^2 : [a> b] • R are convex and have finiteone-sided derivatives i p [ ( a + ) , t p ' 2 ( a + ) , i p ' i ( b — ) , i p ' 2 ( b — ) (cf. [3], also [4] p. 22).There is another characterization of the space B C [ a , 6]. Let V = V { \ a , 6])be a family of all partitionsP = (x0,xi,...,zn),a = xq < x i < . . . < x n = b,n€ Nof the interval [a, 6] such that n > 2 . For an arbitrary function ( p : [a, 6] —> Rand any partition P € V we putr-JX i http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

BC-SOLUTIONS OF NONLINEAR FUNCTIONAL EQUATION—A NONUNIQUENESS CASE

Demonstratio Mathematica , Volume 26 (2): 12 – Apr 1, 1993

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Publisher
de Gruyter
Copyright
© by Tadeusz Kostrzewski
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1993-0202
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XXVINo 21993Tadeusz KostrzewskiJ9C-SOLUTIONS OF N O N L I N E A R F U N C T I O N A LEQUATION—A NONUNIQUENESS CASE1. S o m e properties of B C [ a , b] spaceBy B C [ a , 6] we denote the linear space of all functions <p : [a, 6] —• R ofthe form <p = t p i — i p 2 , where i p 1,^2 : [a> b] • R are convex and have finiteone-sided derivatives i p [ ( a + ) , t p ' 2 ( a + ) , i p ' i ( b — ) , i p ' 2 ( b — ) (cf. [3], also [4] p. 22).There is another characterization of the space B C [ a , 6]. Let V = V { \ a , 6])be a family of all partitionsP = (x0,xi,...,zn),a = xq < x i < . . . < x n = b,n€ Nof the interval [a, 6] such that n > 2 . For an arbitrary function ( p : [a, 6] —> Rand any partition P € V we putr-JX i

Journal

Demonstratio Mathematicade Gruyter

Published: Apr 1, 1993

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