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

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

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

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

in topological vector spaces.

Keywords

Hyers–Ulam stability, quartic mapping, topological vector space

Mathematical Subject Classification 2010

Primary: 39B82

Secondary: 34K20, 54A20

Milestones

Received: 23 January 2013

Accepted: 28 January 2013

Published: 8 October 2013

Communicated by Martin Bohner

Authors

Saeid Ostadbashi
Department of Mathematics Urmia University Urmia 57561-51818 Iran

Abbas Najati
Department of Mathematics Faculty of Mathematical Sciences University of Mohaghegh Ardabili Ardabil 56199-11367 Iran

Mahsa Solaimaninia
Department of Mathematics Urmia University Urmia 57561-51818 Iran

Themistocles M. Rassias
Department of Mathematics Zografou Campus National Technical University of Athens 15780 Athens Greece

Vol. 6, No. 4, 2013

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

Abstract

Keywords

Mathematical Subject Classification 2010

Milestones

Authors