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Generalized Ulam-Hyers Stability of Jensen Functional Equation in Šerstnev PN Spaces
Gordji, M. Eshaghi,Ghaemi, M. B.,Majani, H.,Park, C. Hindawi Publishing Corporation 2010 Journal of inequalities and applications Vol.2010 No.1
<P>We establish a generalized Ulam-Hyers stability theorem in a Šerstnev probabilistic normed space (briefly, Šerstnev PN-space) endowed with ΠM. In particular, we introduce the notion of approximate Jensen mapping in PN-spaces and prove that if an approximate Jensen mapping in a Šerstnev PN-space is continuous at a point then we can approximate it by an everywhere continuous Jensen mapping. As a version of a theorem of Schwaiger, we also show that if every approximate Jensen type mapping from the natural numbers into a Šerstnev PN-space can be approximated by an additive mapping, then the norm of Šerstnev PN-space is complete.</P>
R.R. Rantty,M. Eshaghi,A.M. Ali,F. Jamal,K. Yusoff The Microbiological Society of Korea 2001 The journal of microbiology Vol.39 No.3
Group A Streptococcus strain ST4529 is a provisional new ems type which has been recently reported in Malaysia (Jomal, et al. 1999. Energ. Infect . Dis. 5,10-14). This strain was found to be opacity factor (OF) negative with a Tl phenotype. Usually, OF negative strains with T1 phenotypes are associated with acute rheumatic fever. However, strain ST4529 was isolated from the blood of a patient with septicemia. Comparison of the deduced amino acid sequence of the mature hypervariable N-terminus of ST4529 showed only 43% identity with that of M5, the closest matched OF negative strain with a T1 phenotype. Thus, ST4529 most probably encodes a new serospecifically unique M protein which is associated with septicemia rather than pharyngitis infections. The strains with these phenotypes are very important because their sequences should be considered for developing any anti-streptococcal vaccines.
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>
Coupled Fixed-Point Theorems for Contractions in Partially Ordered Metric Spaces and Applications
Gordji, M. Eshaghi,Cho, Y. J.,Ghods, S.,Ghods, M.,Dehkordi, M. Hadian Hindawi Limited 2012 Mathematical problems in engineering Vol.2012 No.-
<P>Bhaskar and Lakshmikantham (2006) showed the existence of coupled coincidence points of a mappingFfromX×XintoXand a mappinggfromXintoXwith some applications. The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and improve the recent fixed-point theorems due to Bessem Samet (2010). Indeed, we introduce the definition of generalizedg-Meir-Keeler type contractions and prove some coupled fixed point theorems under a generalizedg-Meir-Keeler-contractive condition. Also, some applications of the main results in this paper are given.</P>
On a composite functional equation related to the Golab-Schinzel equation
Madjid Eshaghi Gordji,Themistocles M. Rassias,Mohamed Tial,Driss Zeglami 대한수학회 2016 대한수학회보 Vol.53 No.2
Let $X$ be a vector space over a field $K$ of real or complex numbers and $ k\in \mathbb{N}$. We prove the superstability of the following generalized Golab--Schinzel type equation \begin{equation*} f(x_{1}+\sum_{i=2}^{p}x_{i}f(x_{1})^{k} f(x_{2})^{k}\cdots f(x_{i-1})^{k})=\prod \limits_{i=1}^{p}f(x_{i}),\ x_{1},x_{2},\ldots,x_{p}\in X, \end{equation*} where $f:X\rightarrow K$ is an unknown function which is hemicontinuous at the origin.
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.
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.
ON A COMPOSITE FUNCTIONAL EQUATION RELATED TO THE GOLAB-SCHINZEL EQUATION
Gordji, Madjid Eshaghi,Rassias, Themistocles M.,Tial, Mohamed,Zeglami, Driss Korean Mathematical Society 2016 대한수학회보 Vol.53 No.2
Let X be a vector space over a field K of real or complex numbers and $k{\in}{\mathbb{N}}$. We prove the superstability of the following generalized Golab-Schinzel type equation $f(x_1+{\limits\sum_{i=2}^p}x_if(x_1)^kf(x_2)^k{\cdots}f(x_{i-1})^k)={\limits\prod_{i=1}^pf(x_i),x_1,x_2,{\cdots},x_p{\in}X$, where $f:X{\rightarrow}K$ is an unknown function which is hemicontinuous at the origin.
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 $r\;{\neq}\;{\pm}1$.