THE FUNCTIONAL EQUATION (Á) IS STABLE IF ANY FUNCTION G SATISFYING THE EQUATION (Á)APPROXIMATELY IS NEAR TO THE TRUE SOLUTION OF (Á). A FUNCTIONAL EQUATION IS SUPERSTABLE IF EVERY SOLUTION SATISFYING THE EQUATION APPROXIMATELY IS AN EXACT SOLUTION OF IT.WE STUDY THE STABILITY AND SUPERSTABILITY OF THE GENERALIZED POLYNOMIAL FUNCTIONAL EQUATION OF DEGREE 5.

LET G BE A SIMPLE GRAPH OF ORDER N. THE DOMINATION POLYNOMIAL OF G IS THE POLYNOMIAL (FORMULA) XI, WHERE D (G, I) IS THE NUMBER OF DOMINATING SETS OF G OF SIZE I. LET N AND Q³3 BE ANY POSITIVE INTEGER AND FQ,N BE THE GENERALIZED FRIENDSHIP GRAPH FORMED BY A COLLECTION OF N CYCLES (ALL OF ORDER Q), MEETING AT A COMMON VERTEX. WE STUDY THE DOMINATION POLYNOMIALS OF SOME GENERALIZED FRIENDSHIP GRAPHS. IN PARTICULAR WE EXAMINE THE DOMINATION ROOTS OF THESE FAMILIES, AND FIND THE LIMITING CURVE FOR THE ROOTS.

USING THE FIXED POINT METHOD, WE PROVE THE GENERALIZED HYERS-ULAM STABILITY OF THE FOLLOWING GENERALIZED SEXTIC FUNCTIONAL EQUATION DF (X, Y):= F (MX+ Y) +F (MX- Y) +F(X+ MY) +F(X- MY) - (M4+ M2) [F(X+ Y) +F(X- Y)] - 2(M6- M4- M2+ 1) [F(X) + F(Y)] IN MATRIX FUZZY NORMED SPACES. FURTHERMORE, USING THE FIXED POINT METHOD, WE ALSO PROVE THE HYERS-ULAM STABILITY OF THE ABOVE FUNCTIONAL EQUATION IN MATRIX RANDOM NORMED SPACES.