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Approximation of radical functional equations related to quadratic and quartic mappings
Khodaei, H.,Eshaghi Gordji, M.,Kim, S.S.,Cho, Y.J. Academic Press 2012 Journal of mathematical analysis and applications Vol.395 No.1
In this paper, we introduce and solve of the radical quadratic and radical quartic functional equations: f(ax<SUP>2</SUP>+by<SUP>2</SUP>)=af(x)+bf(y),f(ax<SUP>2</SUP>+by<SUP>2</SUP>)+f(|ax<SUP>2</SUP>-by<SUP>2</SUP>|)=2a<SUP>2</SUP>f(x)+2b<SUP>2</SUP>f(y). We also establish some stability results in 2-normed spaces and then the stability by using subadditive and subquadratic functions in p-2-normed spaces for these functional equations.
Khodaei, M.,Seyyed Ebrahimi, S.A.,Park, Y.J.,Choi, S.H.,Kim, C.,Son, J.,Baik, S. Elsevier Sequoia 2014 THIN SOLID FILMS - Vol.571 No.1
The perfect (111)-oriented Co<SUB>0.8</SUB>Fe<SUB>2.2</SUB>O<SUB>4</SUB> thin films are grown on Pt(111)/Si substrate using pulsed laser deposition technique at substrate temperature of 600<SUP>o</SUP>C and laser pulse rate of 5 and 10Hz. The Fe K-edge X-ray absorption near edge structure analyses revealed that Fe in Co<SUB>0.8</SUB>Fe<SUB>2.2</SUB>O<SUB>4</SUB> films deposited at both 5 and 10Hz exists in Fe<SUP>3+</SUP> state leading to the actual composition of Co<SUB>0.8</SUB>Fe<SUB>2.2</SUB>O<SUB>4+δ</SUB>. In order to study the effect of film thickness on the magnetic properties, the film thickness was increased by increase in the pulse rate as well as the time of deposition during pulsed laser deposition process. It was found that by increase of the film thickness, the saturation magnetization and squareness will be generally increased. In the films with same thickness, those which deposited at higher pulse rate have a higher coercivity. In the films deposited at same pulse rate (10Hz) and different time of deposition, the saturation magnetization, coercivity, and squareness were increased by increasing the thickness, but the coercivity will be decreased with further increasing the thickness due to the relaxation of residual stresses.
Approximate Quartic and Quadratic Mappings in Quasi-Banach Spaces
Gordji, M. Eshaghi,Khodaei, H.,Kim, Hark-Mahn Hindawi Publishing Corporation 2011 International journal of mathematics and mathemati Vol.2011 No.-
<P>we establish the general solution for a mixed type functional equation of aquartic and a quadratic mapping in linear spaces. In addition, we investigate the generalized Hyers-Ulam stability in p-Banach spaces.</P>
박춘길,M. Eshaghi Gordji,H. Khodaei 대한수학회 2010 대한수학회보 Vol.47 No.5
In this paper, we investigate the Cauchy-Rassias stability in Banach spaces and also the Cauchy-Rassias stability using the alternative fixed point for the functional equation:[수식]f(sx + ty 2+ rz) + f(sx + ty 2− rz) + f(sx − ty 2+ rz) + f(sx − ty 2− rz)= s2f(x) + t2f(y) + 4r2f(z)for any fixed nonzero integers s, t, r with r ≠ ±1.
Park, Choon-Kil,Gordji, M. Eshaghi,Khodaei, H. Korean Mathematical Society 2010 대한수학회보 Vol.47 No.5
In this paper, we investigate the Cauchy-Rassias stability in Banach spaces and also the Cauchy-Rassias stability using the alternative fixed point for the functional equation: $$f(\frac{sx+ty}{2}+rz)+f(\frac{sx+ty}{2}-rz)+f(\frac{sx-ty}{2}+rz)+f(\frac{sx-ty}{2}-rz)=s^2f(x)+t^2f(y)+4r^2f(z)$$ for any fixed nonzero integers s, t, r with $r\;{\neq}\;{\pm}1$.