Vol. 6, No. 4, 2013

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A Pexider difference associated to a Pexider quartic functional equation in topological vector spaces

Saeid Ostadbashi, Abbas Najati, Mahsa Solaimaninia and Themistocles M. Rassias

Vol. 6 (2013), No. 4, 505–510

Let (G,+) be an Abelian group and X be a sequentially complete Hausdorff topological vector space over the field of rational numbers. We deal with a Pexider difference

2f(2x + y) + 2f(2x y) 2g(x + y) 2g(x y) 12g(x) + 3g(y),

where f and g are mappings defined on G and taking values in X. We investigate the Hyers–Ulam stability of the Pexiderized quartic functional equation

2f(2x + y) + 2f(2x y) = 2g(x + y) + 2g(x y) + 12g(x) 3g(y)

in topological vector spaces.

Hyers–Ulam stability, quartic mapping, topological vector space
Mathematical Subject Classification 2010
Primary: 39B82
Secondary: 34K20, 54A20
Received: 23 January 2013
Accepted: 28 January 2013
Published: 8 October 2013

Communicated by Martin Bohner
Saeid Ostadbashi
Department of Mathematics
Urmia University
Urmia 57561-51818
Abbas Najati
Department of Mathematics
Faculty of Mathematical Sciences
University of Mohaghegh Ardabili
Ardabil 56199-11367
Mahsa Solaimaninia
Department of Mathematics
Urmia University
Urmia 57561-51818
Themistocles M. Rassias
Department of Mathematics
Zografou Campus
National Technical University of Athens
15780 Athens