In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...

*Correspondence: [email protected] 2Department of Mathematics, University of Zagreb, Zagreb, Croatia Full list of author information is available at the end of the article Abstract We consider quasilinearity of the functional (h ◦ v) · ( ◦ gv ), where is a monotone h-concave (h-convex) function, v and g are functionals with certain super(sub)additivity properties. Those general results are appli...

the stability problem of the functional equation was conjectured by ulam and was solved by hyers in the case of additive mapping. baker et al. investigated the superstability of the functional equation from a vector space to real numbers.in this paper, we exhibit the superstability of $m$-additive maps on complete non--archimedean spaces via a fixed point method raised by diaz and margolis.

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We introduce a novel parametric family of symmetric information-theoretic distances based on Jensen’s inequality for a convex functional generator. In particular, this family unifies the celebrated Jeffreys divergence with the Jensen-Shannon divergence when the Shannon entropy generator is chosen. We then design a generic algorithm to compute the unique centroid defined as the minimum average d...