Nearly Quartic Mappings in β-Homogeneous F-Spaces

In this paper, we investigate the Hyers–Ulam stability of the following quartic equation $$\begin{array}{ll} {\sum\limits^{n}_{k=2}}\left({\sum\limits^{k}_{i_{1}=2}}{\sum\limits^{k+1}_{i_{2}=i_{1}+1}} \ldots {\sum\limits^{n}_{i_{n-k+1}=i_{n-k}+1}}\right)\\ \quad\times f \left({\sum\limits^{n}_{i=1,i \neq i_{1},\ldots,i_{n-k+1}}} x_{i}-{\sum\limits^{n-k+1}_{r=1}}x_{i_{r}}\right) + f \left({\sum\limits^{n}_{i=1}}x_{i}\right)\\ \quad-2^{n-2}{\sum\limits^{}_{1 \leq{i} \leq{j} \leq{n}}}(f(x_{i} + x_{j}){+f(x_{i} - x_{j})){+2^{n-5}(n - 2){\sum\limits^{n}_{i=1}}f(2x_{i})}} = \theta \end{array} $$ $({n \in \mathbb{N}, n \geq 3})$ in β-homogeneous F-spaces.     

Corrigendum to “Property (gb) and perturbations” [J. Math. Anal. Appl. 383 (1) (2011) 82–94]

We give a complete reference for work cited in [M.H.M. Rashid, Property (gb) and perturbations, J. Math. Anal. Appl. 383 (1) (2011) 82–94].     

Erratum to: “Local edge domination critical graphs” [Discrete Math. 161 (1996) 175–184]

The proof of the main theorem in the paper Henning et al. (1996) [2] is incorrect as it is missing an important case. Here we complete the proof by giving the missing case.