@article{Alsaeed2026, 
author = {Salman Alsaeed and El-sayed El-hady and Janusz Brzdęk},
title = {On Ulam stability of generalized Hosszú functional equation},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {4},
pages = {11332-11346},
keywords = {functional equations, Ulam stability, Hosszúequation, m-norm},
url = {https://www.sciopen.com/article/10.3934/math.2026466},
doi = {10.3934/math.2026466},
abstract = {We investigated Hyers-Ulam stability (H-US) of the following generalization of the Hosszú equation (HFE):      Υ  (      x    1    +      x    2    −  α      x    1        x    2    )  +  Υ  (  α      x    1        x    2    )  =  Υ  (      x    1    )  +  Υ  (      x    2    ), in the class of maps    Υ from a quadratically closed field        K   into a linear space, where    α  ∈      K   is fixed. We considered this stability in cases where the linear space is equipped with either the    m-norm or the classical norm. In this way, we extended some earlier stability outcomes obtained for maps from the set of reals        R   into a Banach space. We also proved some auxiliary stability results for the Cauchy additive equation    ψ  (  x  +  y  )  =  ψ  (  x  )  +  ψ  (  y  ) in    m-Banach spaces. Finally, we discussed the symmetry issues that can be observed in these results.}
}