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Ghaemi, Mohammad Bagher,Choubin, Mehdi,Saadati, Reza,Park, Choonkil,Shin, Dong Yun Eudoxus Press LLC 2016 Journal of computational analysis and applications Vol.21 No.1
<P>In this paper, we present a fixed point method to prove the Hyers-Ulam stability of the system of Euler-Lagrange quadratic-quartic functional equations {f(ax(1) + bx(2), y) + f(bx(1) + ax(2), y) + ab f(x(1) - x(2), y) = (a(2) + b(2))[f(x(1), y) + f(x(2), y)] + 4ab f(x(1)+x(2)/2, y), f(x, ay(1) + by(2)) + f(x, by(1) + ay(2)) + 1/2ab(a - b)(2) f(x, y(1) - y(2)) = (a(2) -b(2))(2)[f(x, y(1)) + f(x, y(2))] + 8ab f(x, y(1)+y(2)/2) for all numbers a and b with a + b is not an element of {0, +/- 1}, ab + 2 not equal 2(a + b)(2) and ab(a - b)(2) + 4 not equal 4(a + b)(4) in Archimedean and non-Archimedean Banach spaces and we show that the approximation in non-Archimedean Banach spaces is better than the approximation in (Archimedean) Banach spaces.</P>
A Fixed Point Approach to Stability of Quintic Functional Equations in Modular Spaces
GHAEMI, MOHAMMAD BAGHER,CHOUBIN, MEHDI,SADEGHI, GHADIR,GORDJI, MADJID ESHAGHI Department of Mathematics 2015 Kyungpook mathematical journal Vol.55 No.2
In this paper, we present a fixed point method to prove generalized Hyers-Ulam stability of the systems of quadratic-cubic functional equations with constant coefficients in modular spaces.