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- W2727858468 abstract "The aim of this paper is to investigate generalized Ulam-Hyers stabilities of the following Euler-Lagrange-Jensen-$(a,b)$-sextic functional equation $$ f(ax+by)+f(bx+ay)+(a-b)^6left[fleft(frac{ax-by}{a-b}right)+fleft(frac{bx-ay}{b-a}right)right] = 64(ab)^2left(a^2+b^2right)left[fleft(frac{x+y}{2}right)+fleft(frac{x-y}{2}right)right] +2left(a^2-b^2right)left(a^4-b^4right)[f(x)+f(y)] $$ where $aneq b$, such that $kin mathbb{R}$; $k=a+bneq 0,pm1$ and $lambda=1+(a-b)^6-2left(a^6+b^6right)-62(ab)^2left(a^2+b^2right)neq 0$, in quasi-$beta$-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-$beta$-normed spaces by using fixed point method. A counter-example for a singular case is also indicated." @default.
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- W2727858468 date "2017-06-28" @default.
- W2727858468 modified "2023-09-28" @default.
- W2727858468 title "Generalized Stabilities of Euler-Lagrange-Jensen (a,b)-Sextic Functional Equations in Quasi-β-Normed Spaces" @default.
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