Malaya Journal of Matematik, Vol. 9, No. 1, 217-243, 2021 https://doi.org/10.26637/MJM0901/0038 Stabilities of mixed type Quintic-Sextic functional equations in various normed spaces John Micheal Rassias1, Elumalai Sathya2, Mohan Arunkumar 3* Abstract In this paper, we introduce ”Mixed Type Quintic - Sextic functional equations” and then provide their general solution, and prove generalized Ulam - Hyers stabilities in Banach spaces and Fuzzy normed spaces, by using both the direct Hyers - Ulam method and the alternative fixed point method. Keywords Quintic functional equation, sextic functional equation, mixed type quintic - sextic functional equation, generalized Ulam - Hyers stability, Banach space, Fuzzy Banach space, Hyers - Ulam method, alternative fixed point method. AMS Subject Classification 39B52, 32B72, 32B82. 1Pedagogical Department - Mathematics and Informatics, The National and Kapodistrian University of Athens,4, Agamemnonos Str., Aghia Paraskevi, Athens 15342, Greece. 2Department of Mathematics, Shanmuga Industries Arts and Science College, Tiruvannamalai - 606 603, TamilNadu, India. 3Department of Mathematics, Government Arts College, Tiruvannamalai - 606 603, TamilNadu, India. *Corresponding author: 1
[email protected]; 2
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[email protected] Article History: Received 11 December 2020; Accepted 24 January 2021 c 2021 MJM. Contents such problems the interested readers can refer the monographs of [1,4,5,8, 18, 22, 24–26, 33, 36, 37, 41, 43, 48]. 1 Introduction.......................................217 The general solution of Quintic and Sextic functional 2 General Solution..................................218 equations 3 Stability Results In Banach Space . 219 f (x + 3y) − 5 f (x + 2y) + 10 f (x + y) − 10 f (x) 3.1 Hyers - Ulam Method.................. 219 + 5 f (x − y) − f (x − 2y) = 120 f (y) (1.1) 3.2 Alternative Fixed Point Method..........