Orthogonally additive-additive and orthogonally quadratic-quadratic functional equation in orthogonality spaces
Orthogonally additive-additive and orthogonally quadratic-quadratic functional equation in orthogonality spaces
Abstract Using fixed point method, we prove the Hyers-Ulam stability of the orthogonally additive-additive and orthogonally quadratic-quadratic functional equation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mi>f</mml:mi> <mml:mfenced> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>+</mml:mo> <mml:mi>y</mml:mi> <mml:mo>+</mml:mo> <mml:mi>z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:mfenced> <mml:mo>+</mml:mo> <mml:mi>f</mml:mi> <mml:mfenced> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>+</mml:mo> …