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APPROXIMATELY QUINTIC AND SEXTIC MAPPINGS ON THE PROBABILISTIC NORMED SPACES
Ghaemi, Mohammad Bagher,Majani, Hamid,Gordji, Majid Eshaghi Korean Mathematical Society 2012 대한수학회보 Vol.49 No.2
We prove the stability for the systems of quadratic-cubic and additive-quadratic-cubic functional equations with constant coefficients on the probabilistic normed spaces (briefly PN spaces).
APPROXIMATELY QUINTIC AND SEXTIC MAPPINGS ON THE PROBABILISTIC NORMED SPACES
Mohammad Bagher Ghaemi,Hamid Majani,Majid Eshaghi Gordji 대한수학회 2012 대한수학회보 Vol.49 No.2
We prove the stability for the systems of quadratic-cubic and additive-quadratic-cubic functional equations with constant coefficients on the probabilistic normed spaces (briefly PN spaces).
A General System of Nonlinear Functional Equations in Non-Archimedean Spaces
Ghaemi, Mohammad Bagher,Majani, Hamid,Gordji, Madjid Eshaghi Department of Mathematics 2013 Kyungpook mathematical journal Vol.53 No.3
In this paper, we prove the generalized Hyers-Ulam-Rassias stability for a system of functional equations, called general system of nonlinear functional equations, in non-Archimedean normed spaces and Menger probabilistic non-Archimedean normed spaces.
Fahandari Heidar Kermanizadeh,Majani Hamid,Jang Sun Young,Park Choonkil 경남대학교 수학교육과 2019 Nonlinear Functional Analysis and Applications Vol.24 No.3
In this paper, we introduce the following functional equation \begin{equation*}\label{000} \sum_{i=0}^{k}(-1)^i\left(% \begin{array}{c} k \\ i \\ \end{array}% \right)f(x+(j-i)y)=k!f(y) . \end{equation*} where $k\in\mathbb{N}$ and $j=[\frac{k+1}{2}]$. We achieve the general solution of the above functional equation.
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>