Revista de la
Unión Matemática Argentina
Almost additive-quadratic-cubic mappings in modular spaces
Mohammad Maghsoudi, Abasalt Bodaghi, Abolfazl Niazi Motlagh, and Majid Karami
Volume 60, no. 2 (2019), pp. 359–379     Online first

https://doi.org/10.33044/revuma.v60n2a05

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Abstract

We introduce and obtain the general solution of a class of generalized mixed additive, quadratic and cubic functional equations. We investigate the stability of such modified functional equations in the modular space $X_\rho$ by applying the $\Delta_2$-condition and the Fatou property (in some results) on the modular function $\rho$. Furthermore, a counterexample for the even case (quadratic mapping) is presented.