Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 2001. Sectio Mathematicae (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 28)
Kocsis, I., On the stability of a sum form functional equation of multiplicative type
On the stability of a sum form functional equation of multiplicative type 49 that is, E /(ppo = E /Cpo - /(p) E m2(pí)) + a 1(p, p) + b 1(p, p) + lap). i = 1 i = 1 Putting this into (2.2) and collecting the terms symmetric in P and Q on the left hand side we get 771 m m m E E /Ow) - /(p) E m2(po E i=i j =1 i=i j =1 m m X] Mi ( P i )^/(^) + E ) E (?i) i = 1 j = 1 2 = 1 ,7 = 1 = MI(P) + A 1(p, P) MÁ (li)) + hip) Y, M j= 1 j= 1 m + Ai(p, Q) + J] h(pPi,Q ) + mii(Q). 1 = 1 j = l Since the right hand side is also simmetric in P and Q we have Ai(p,P) X>3(9i)- 1 i = l E M2(Pi)-l = Mi(p) E A/ /i (?;) E ) + E m2 (P 1' ) E /fe ) i=l i=l i = l (2.3) - E Mi ) E /(?;) - E m2 ) E /(pi ) t=i i=i j=i i = l - Lx(Q) M 2( P i) - L^P) J2 M 2( q j ) £ = 1 J=1 + tl(p, Q) E M2(Pi) - 6l(P' E + £ &i(p 9 i , P) - X) Q) + mMP) - mL^Q). j=i i=l
