Stabilities and counter-examples of mixed Euler-Lagrange $k$-cubic-quartic functional equation in quasi-$\beta$-normed spaces


JOhn Michael Rassias - Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, Agamemnonos Str., Aghia Paraskevi, Athens, Attikis 15342, Greece.
Beri Venkatachalapathy Senthil Kumar - Department of Mathematics, C. Abdul Hakeem College of Engineering Technology, Melvisharam-632 509, Tamil Nadu, India.
Sriramulu Sabarinathan - Department of Mathematics, SRM Institute of Science Technology, Kattankulthur-603 203, Tamil Nadu, India.


The intention of this study is to introduce a new mixed Euler-Lagrange $k$-cubic-quartic functional equation and then to solve it for general solution. We study its various stabilities in quasi-$\beta$-normed spaces using fixed point technique, as well. We also provide counter-examples to show that the above equation is not stable for singular cases.


Cubic mapping, quartic mapping, quasi-$\beta$-normed space