On Pexider Differences in Topological Vector Spaces - Abbas Najati; M. R. Abdollahpour; Gwang Hui Kim (Abstract and Applied Analysis)
Let 𝑋 be a normed space and 𝑌 a sequentially complete Hausdorff topological vector space over the field ℚ of rational numbers. Let 𝐷1={(𝑥,𝑦)∈𝑋×𝑋∶‖𝑥‖+‖𝑦‖≥𝑑}, and 𝐷2={(𝑥,𝑦)∈𝑋×𝑋∶‖𝑥‖+‖𝑦‖<𝑑} where 𝑑>0. We prove that the Pexiderized Jensen functional equation is stable for functions defined on 𝐷1(𝐷2), and taking values in 𝑌. We consider also the Pexiderized Cauchy functional equation.