in this paper we investigate the generalized hyers-ulamstability of the following cauchy-jensen type functional equation$$qbig(frac{x+y}{2}+zbig)+qbig(frac{x+z}{2}+ybig)+qbig(frac{z+y}{2}+xbig)=2[q(x)+q(y)+q(z)]$$ in non-archimedean spaces

In this article, a new class of functional models in which smoothing splines are used to model fixed effects as well as random effects is introduced. The linear mixed effects models are extended to nonparametric mixed effects models by introducing functional random effects, which are modeled as realizations of zero-mean stochastic processes. The fixed functional effects and the random functiona...

We propose an extensive framework for additive regression models for correlated functional responses, allowing for multiple partially nested or crossed functional random effects with flexible correlation structures for, e.g., spatial, temporal, or longitudinal functional data. Additionally, our framework includes linear and nonlinear effects of functional and scalar covariates that may vary smo...

In  this paper, we investigate the generalizedHyers-Ulam-Rassias stability for the quartic, cubic and additivefunctional equation$$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+(k^2-1)[k^2f(y)+k^2f(-y)-2f(x)]$$ ($k in mathbb{Z}-{0,pm1}$) in $p-$Banach spaces.

‎In this paper‎, ‎we present the‎ generalized hyperstability results of cubic functional equation in‎ ‎ultrametric Banach spaces using the fixed point method‎.