A FIXED POINT APPROACH TO STABILITY OF A CUBIC FUNCTIONAL EQUATION IN 2-BANACH SPACES
Abstract
In this paper, we prove a new type of stability and hyperstability results for
the following cubic functional equation
f (2x + y) + f (2x - y) = 2f (x + y) + 2f (x - y) + 12f(x)
in 2-Banach spaces using fixed point approach.
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bibitem{aoki} T. Aoki : textit{On the stability of the linear transformation in Banach spaces}. J. Math. Soc. Japan, {bf 2},(1950), 64-66.
bibitem{brzdek1} J. Brzdc{e}k : textit{A note on stability of additive mappings. In Stability of Mappings of Hyers-Ulam Type}. Edited by: Rassias, T.M., Tabor, J. Hadronic Press, Palm Harbor, (1994), 19-22.
bibitem{brzdek4} Brzdc{e}k, J. : textit{Hyperstability of the Cauchy equation on restricted domains}. Mathematical Analysis and Applications, Acta Math. Hungr. {bf 141} (1-2), (2013), 58–67.
bibitem{breci3} J. Brzdc{e}k, K. Ciepli'{n}ski : textit{On a fixed point theorm in 2-Banach spaces and some of its applications}. Acta Math. Sci. {bf 38 B}(2), (2018), 377-390.
bibitem{breci4} J. Brzdc{e}k, E. S. El-hady : textit{On Approximately additive mappings in 2-Banach spaces }, Bull. Aust. Math. Soc.{bf 376}, 193 (2019)
bibitem{Freese} R. E. Freese,Y. J. Cho : textit{Geometry of Linear 2-normed Spaces}. Hauppauge, NY: Nova Science Publishers,
Inc, 2001.
bibitem{gajda} Z. Gajda : textit{On stability of additive mappings}. Int. J. Math. Math. Sci. {bf 14}, (1991), 431-434.
bibitem{hyers} D. H. Hyers : textit{On the stability of the linear functional equation}. Proc. Natl. Acad. Sci.
USA textbf{27}, (1941), 222-224.
bibitem{jun0} K.-W. Jun, H.-M. Kim : textit{The generalized Hyers-Ulam–Rassias stability of a cubic functional equation}. J. Math. Anal. Appl.
{bf 274 }, (2002), 867-878.
bibitem{mir} AK. Mirmostafaee , MS. Moslehian : textit{Fuzzy approximately cubic mappings}. Inf. Sci. {bf 178}, 3791-3798 (2008)
bibitem{mursaleen} M. Mursaleen , SA. Mohiuddine : textit{ On stability of a cubic functional equation in intuitionistic fuzzy normed spaces}. Chaos Solitons Fractals, {bf 42}, (2009), 2997-3005.
bibitem{park} W.-G. Park : textit{Approximate additive mappings in 2-Banach spaces and related topics}. J. Math. Anal. Appl.
{bf 376}, (2011), 193-202.
bibitem{rassias1} T.M. Rassias : textit{On the stability of the linear mapping in Banach spaces}. Proc. Am.
Math. Soc. textbf{72}, (1978), 297-300.
bibitem{ras3} T.M. Rassias : textit{On a modified Hyers-Ulam sequence}. J. Math. Anal. Appl. {bf 158}, (1991),
-113.
bibitem{ras4} Rassias, T.M., Semrl, P.: textit{On the behavior of mappings which do not satisfy
Hyers–Ulam stability}. Proc. Am. Math. Soc. {bf 114}, 989-993 (1992)
% bibitem{sayar} K.Y.N. Sayar, A. Bergam, : textit{Some hyperstability results for a Cauchy-Jensen
%type functional equation in 2-Banach spaces}. Proyecciones J. of Math. {bf 39}(1), (2020), 73-89.
bibitem{sayar3} K.Y.N. Sayar, A. Bergam : textit{ Approximate solutions of a quadratic functional equation in 2-Banach spaces using fixed point theorem}. J. Fixed Point Theory Appl. {bf 22}, Article No. 3. (2020)
bibitem{ulam} S.M. Ulam : textit{Problems in Modern Mathematics}. Science Editions, John-Wiley $&$ Sons
Inc., New York, (1964)
DOI: https://doi.org/10.22190/FUMI210426017S
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