Exploring the stability of two different forms of a same functional equation
DOI:
https://doi.org/10.56405/dngcrj.2024.09.01.03Keywords:
Reciprocal functional Equation, Hyers-Ulam-Rassias Stability, Banach Space, General Solutions, Direct MethodAbstract
Within this manuscript, we shall delve into the direct method and explore the general solution as well as the classical stability of the ensuing reciprocal functional equation
[f(x-y+z)-f(3x+y-z)][f(x+y-z)+2f(x-y+z)]-2f(x-y+z)^2=0
in Banach spaces. Moreover, another objective of this work is to obtain another interesting result of stability of the same equation but this time, we make a little change of the above equation and we obtain a new stability result however with a supplementary condition on the mapping f.
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