Non-stabilities of mixed type Euler-Lagrange k-cubic-quartic functional equation in various normed spaces

Mathematical Analysis and its Contemporary Applications

دوره 1، شماره 1، اردیبهشت 2019، صفحه 1-43   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/maca.2019.679849

نویسندگان

John Michael Rassias¹؛ Mohan Arunkumar^{* 2}؛ Elumalai Sathya³

¹Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, 4, Agamemnonos Str. Aghia Paraskevi, Athens 15342, Greece.

²Department of Mathematics, Government Arts College, Tiruvannamalai - 606 603, TamilNadu, India.

³Department of Mathematics, Shanmuga Industries Arts and Science College, Tiruvannamalai - 606 603, TamilNadu, India.

چکیده

In this paper, we introduce and examine the generalized Ulam-Hyers stability of fixed Euler-Lagrange  k-Cubic-Quartic functional Equation
f(x+ky) + f(kx+y) + f(x-ky) + f(y-kx) = k²[2f(x+y) + f(x-y) + f(y-x)] + 2(k⁴-1) [f(x) + f(y)] +k²/4(k²-1) [f(2x) + f(2y)]
where k is a real number with k ≠ 0, ±1 in various Banach spaces with the help of two different methods.

کلیدواژه‌ها

Cubic functional equation؛ quartic functional equations؛ mixed type functional equations؛ Generalized Hyers-Ulam stability؛ Banach space؛ Quasi-Beta Banach space؛ Fuzzy Banach space