Journal of Mathematical Physics, Analysis, Geometry
2021, vol. 17, No 3, pp. 341-368   https://doi.org/10.15407/mag17.02.341     ( to contents , go back )
https://doi.org/10.15407/mag17.02.341

Stability of Complex Functional Equations in 2-Banach Spaces

Anshul Rana

School of Mathematics, Thapar Institute of Engineering & Technology, Patiala-147004, India
E-mail: anshulrana44572@gmail.com

Ravinder Kumar Sharma

School of Mathematics, Thapar Institute of Engineering & Technology, Patiala-147004, India
E-mail: ravindersharma880@gmail.com

Sumit Chandok

School of Mathematics, Thapar Institute of Engineering & Technology, Patiala-147004, India
E-mail: sumit.chandok@thapar.edu

Received July 1, 2020, revised March 21, 2021.

Abstract

In the paper, we obtain some results for the Hyers–Ulam stability of the following functional equations:

q(x + iy) + q(xiy) + q(y + ix) + q(yix) = 2q(x) + 2q(y)

and

q(x + iy) + q(xiy) + q(y + ix) + q(yix) = 0

in the setting of 2-Banach spaces.

Mathematics Subject Classification 2010: 39B32, 39B72, 39A45
Key words: 2-normed spaces, 2-Banach space, Hyers–Ulam–Rassias stability, additive mapping, quadratic equation

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