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

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

doi:10.2140/involve.2013.6.505

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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

DOI: 10.2140/involve.2013.6.505

Abstract

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