Stability of the Multi-Jensen Equation

On an equation characterizing multi-Jensen-quadratic mappings and its Hyers–Ulam stability via a fixed point method

“…Our results are significant supplements and/or generalizations of some results from [1,12,13,14,16,18,23,27,29,30,31].…”

Some remarks on the stability of the multi-Jensen equation

“…Since W is complete, it is enough to show that this sequence is Cauchy. Fixing ∈ N and using some results from [9] (which hold true also in the case V instead of the special case V considered there) we see that…”

“…Using this Jensen operator the property of to be multi-Jensen may be expressed as J = 0. In [9] the following stability result for multi-Jensen functions was proved. The next section contains a result concerning the condition J ( ) ≤ ( ) for a more general .…”

Stability of the multi-Jensen equation

“…In 2008 (see [14]) W. Prager and J. Schwaiger proved the Hyers-Ulam stability of multi-Jensen equation, whereas the author (see [4]) showed its stability in the spirit of P. Gavruta (see [6]). …”