We introduce an extended Jensen equation where q > 1 and n are fixed positive integers. We investigate the stability and the asymptotic behavior of the above extended Jensen equation and prove that if 0 < p < 1 and f is a mapping from a normed space into a Banach space with f(0) = 0 which p-asymptotically satisfies the above equation, then it is p-asymptotic close to a linear mapping.

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