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ON SOLUTIONS OF SOME SYSTEM OF FUNCTIONAL EQUATIONS

ON SOLUTIONS OF SOME SYSTEM OF FUNCTIONAL EQUATIONS DEMONSTRATE MATHEMATICAVol. XXXINo 21998Stanislaw MiduraO N S O L U T I O N S OF S O M E S Y S T E MOF F U N C T I O N A L E Q U A T I O N SLet us denote by R the set of real numbers and let Ro = R \ {0}. Inpaper [7] (p. 79), the following system of functional equations(1)F{yixuyix2+ y2x$ + 4xiF(y1,y2)g(xux2)+6xlg(y1,y2)F{x1,(2)+2x2) + 3F(Vl, y2)F (x ux2))yiF(xi,x2)+ xjF(y1,y2)g{y\X\,y\x2+ y2x\ + 4x1F{yi,y2)g{xi,x2),+2+Qxlg(y1,y2)F(x1,x2)+ 3F(y1,y2)F (x1,x2))yig(xi,x2)y2)F{x i, x 2 ) ++ 3x\F(yi,==x\g(yi,,y2)in the class of functions F : Ro x R—t-R, g : Ro x R—>R was consideredand two solutions F ( X I , X 2 ) = g(xi,x2) = 0 for any x\, x2, and F(xi,x2) =g(xi,x2) = | ( x i — x j ) , where pointed out.In the present paper we shall show that the system (1), (2) has also othersolutions in certain classes of functions.The system (1), (2) appeared when some subsemigroups of the group L\were determined. The definition of L\ one can find in [2]. In papers [1]-[16]the authors dealt with the determination of subgroups and subsemigroupsby means of functional equations.First let us http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON SOLUTIONS OF SOME SYSTEM OF FUNCTIONAL EQUATIONS

Demonstratio Mathematica , Volume 31 (2): 6 – Apr 1, 1998

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Publisher
de Gruyter
Copyright
© by Stanislaw Midura
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1998-0207
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATE MATHEMATICAVol. XXXINo 21998Stanislaw MiduraO N S O L U T I O N S OF S O M E S Y S T E MOF F U N C T I O N A L E Q U A T I O N SLet us denote by R the set of real numbers and let Ro = R \ {0}. Inpaper [7] (p. 79), the following system of functional equations(1)F{yixuyix2+ y2x$ + 4xiF(y1,y2)g(xux2)+6xlg(y1,y2)F{x1,(2)+2x2) + 3F(Vl, y2)F (x ux2))yiF(xi,x2)+ xjF(y1,y2)g{y\X\,y\x2+ y2x\ + 4x1F{yi,y2)g{xi,x2),+2+Qxlg(y1,y2)F(x1,x2)+ 3F(y1,y2)F (x1,x2))yig(xi,x2)y2)F{x i, x 2 ) ++ 3x\F(yi,==x\g(yi,,y2)in the class of functions F : Ro x R—t-R, g : Ro x R—>R was consideredand two solutions F ( X I , X 2 ) = g(xi,x2) = 0 for any x\, x2, and F(xi,x2) =g(xi,x2) = | ( x i — x j ) , where pointed out.In the present paper we shall show that the system (1), (2) has also othersolutions in certain classes of functions.The system (1), (2) appeared when some subsemigroups of the group L\were determined. The definition of L\ one can find in [2]. In papers [1]-[16]the authors dealt with the determination of subgroups and subsemigroupsby means of functional equations.First let us

Journal

Demonstratio Mathematicade Gruyter

Published: Apr 1, 1998

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