The aim of this paper is to investigate generalized Ulam-Hyers stabilities of the following Euler-Lagrange-Jensen-(a,b)-sextic functional equation f(ax+by)+f(bx+ay)+(a−b)6[f(a−bax−by​)+f(b−abx−ay​)]=64(ab)2(a2+b2)[f(2x+y​)+f(2x−y​)]+2(a2−b2)(a4−b4)[f(x)+f(y)] where aî€ =b, such that k∈R; k=a+bî€ =0,±1 and λ=1+(a−b)6−2(a6+b6)−62(ab)2(a2+b2)î€ =0, in quasi-β-normed spaces by using fixed point method. In particular, we prove generalized stabilities involving the sum of powers of norms, product of powers of norms and the mixed product-sum of powers of norms of the above functional equation in quasi-β-normed spaces by using fixed point method. A counter-example for a singular case is also indicated
The aim of this paper is to investigate generalized Ulam-Hyers stabilities of the following Euler-Lagrange-Jensen-(a,b)-sextic functional equation f(ax+by)+f(bx+ay)+(a−b)6[f(a−bax−by​)+f(b−abx−ay​)]=64(ab)2(a2+b2)[f(2x+y​)+f(2x−y​)]+2(a2−b2)(a4−b4)[f(x)+f(y)] where aî€ =b, such that k∈R; k=a+bî€ =0,±1 and λ=1+(a−b)6−2(a6+b6)−62(ab)2(a2+b2)î€ =0, in quasi-β-normed spaces by using fixed point method. In particular, we prove generalized stabilities involving the sum of powers of norms, product of powers of norms and the mixed product-sum of powers of norms of the above functional equation in quasi-β-normed spaces by using fixed point method. A counter-example for a singular case is also indicated