arXiv subjects
Publications and source records attributed to M. Eshaghi Gordji.
In this paper, we establish the generalized Hyers-Ulam stability of Jordan homomorphisms and Jordan derivations between ternary algebras via the generalized Jensen equation $rf(\frac{sx+ty}{r})=sf(x)+tf(y)$.
Let $P(z)$ be a polynomial of degree $n\geq 1$. In this paper we define an operator $B$, as following, $$B[P(z)]:=λ_0 P(z)+λ_1 (\frac{nz}{2}) \frac{P'(z)}{1!}+λ_2 (\frac{nz}{2})^2 \frac{P''(z)}{2!},$$ where $λ_0,λ_1$ and $λ_2$ are such that all the zeros of $$u(z)=λ_0 +c(n,1)λ_1 z+c(n,2) λ_2 z^2$$ lie in half plane $$|z|\leq |z-\frac{n}{2}|$$ and obtain a new generalization of some well-known results.
The object of this paper is studying some properties of meromorphic functions which satisfy in the condition \[Re(zf(z)) > α|z^2f'(z)+zf(z)| .\] Parallel results for some related classes are also obtained.
In this paper by making use of the generalized Bernardi - Libera - Livingston integral operator we introduce and study some new subclasses of univalent functions. Also we investigate the relations between those classes and the classes which are studied by Jin-Lin Liu.
In this paper, we investigate the generalized Hyers--Ulam--Rassias stability of the system of functional equations $$f(xy)=f(x)f(y), \qquad\qquad. f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x), $$ on Banach algebras. Indeed we establish the superstability of above system by suitable control functions.
Let $\mathcal A$ be a von Neumann algebra and $\mathcal M$ be a Banach $\mathcal A-$module. It is shown that for every homomorphisms $σ, τ$ on $\mathcal A$, every bounded linear map $f:\mathcal A\to \mathcal M$ with property that $f(p^2)=σ(p)f(p)+f(p)τ(p)$ for every projection $p$ in $\mathcal A$ is a $(σ,τ)-$derivation. Also, it is shown that a bounded linear map $f:\mathcal A \to \mathcal M $ which satisfies $f(ab)= σ(a)f(b)+f(a)τ(b)$ for all $a,b\in \mathcal A$ with $ab=S$, is a $(σ,τ)-$ derivation if $τ(S)$ is left invertible for fixed $S$.
In this paper we investigate the generalized Hyers- Ulam stability of the functional equation $$f (2x +y)+f (2x -y)= f (x + y)+ f (x -y)+2f (2x)-2f (x)$$ in fuzzy Banach spaces.
In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation $$3(f(x+2y)+f(x-2y))=12(f(x+y)+f(x-y))+4f(3y)-18f(2y)+36f(y)-18f(x).$$
We prove generalized Hyres-Ulam-Rassias stability of the cubic functional equation $f(kx+y)+f(kx-y)=k[f(x+y)+f(x-y)]+2(k^3-k)f(x)$ for all $k\in \Bbb N$ and the quartic functional equation $f(kx+y)+f(kx-y)=k^2[f(x+y)+f(x-y)]+2k^2(k^2-1)f(x)-2(k^2-1)f(y)$ for all $k\in \Bbb N$ in non-Archimedean normed spaces.
Let $A$ be an algebra and let $X$ be an $A$-bimodule. A $\Bbb C-$linear mapping $d:A \to X$ is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) $δ:A \to X$ such that $d(a^2)=ad(a)+δ(a)a$ for all $a \in A.$ The main purpose of this paper to prove the Hyers-Ulam-Rassias stability and superstability of the generalized Jordan derivations.
In this paper, we establish the general solution of the functional equation $$f(nx+y)+f(nx-y)=n^2f(x+y)+n^2f(x-y)+2(f(nx)-n^2f(x))-2(n^2-1)f(y)\eqno {0 cm}$$for fixed integers $n$ with $n\neq0,\pm1$ and investigate the generalized Hyers-Ulam-Rassias stability of this equation in quasi-Banach spaces.
In this paper, we obtain the general solution and the generalized Ulam-Hyers stability of the cubic and quartic functional equation &4(f(3x+y)+f(3x-y))=-12(f(x+y)+f(x-y)) &+12(f(2x+y)+f(2x-y))-8f(y)-192f(x)+f(2y)+30f(2x).
In this paper, we achieve the general solution and the generalized Hyers-Ulam-Rassias stability for the quadratic type functional equation &f(x+y+2cz)+f(x+y-2cz)+c^2f(2x)+c^2f(2y) &=2[f(x+y)+c^2f(x+z)+c^2f(x-z)+c^2f(y+z)+c^2f(y-z)] {2.6 cm} for fixed integers $c$ with $c\neq0,\pm1$, by using the fixed point alternative.
Let $A,B$ be two rings and let $ X$ be an $ A-$module. An additive map $h: A\to B$ is called n-ring homomorphism if $h(Π^n_{i=1}a_i)=Π^n_{i=1}h(a_i),$ for all $a_1,a_2, ...,a_n \in {A}$. An additive map $D: A\to X$ is called $n$-ring derivation if $$D(Π^n_{i=1}a_i)=D(a_1)a_2... a_n+a_1D(a_2)a_3... a_n+... +a_1a_2... a_{n-1}D(a_n),$$ for all $a_1,a_2, ...,a_n \in {\mathcal A}$. In this paper we investigate the Hyers-Ulam-Rassias stability of $n$-ring homomorphisms and n-ring derivations.
In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation $$f(2x+y)+f(2x-y)=4(f(x+y)+f(x-y))-{3/7}(f(2y)-2f(y))+2f(2x)-8f(x).$$
In this paper, we investigate Jordan *-homomorphisms on $C^*$-algebras associated with the following functional inequality $\|f(\frac{b-a}{3})+f(\frac{a-3c}{3})+f(\frac{3a+3c-b}{3})\| \leq \|f(a)\|.$ We moreover prove the superstability and the generalized Hyers-Ulam stability of Jordan *-homomorphisms on $C^*$-algebras associated with the following functional equation $$f(\frac{b-a}{3})+f(\frac{a-3c}{3})+f(\frac{3a+3c-b}{3})=f(a).$$
In this paper, we achieve the general solution and the generalized Hyers-Ulam-Rassias stability of the following functional equation $$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+2(1-k^2)f(x)\eqno {2 cm}$$for fixed integers $k$ with $k\neq0,\pm1$ in the quasi-Banach spaces.
In this paper, we investigate homomorphisms between $C^*$-ternary algebras and derivations on $C^*$-ternary algebras, associated with the following functional equation $$f(\frac{x_2-x_1}{3})+f(\frac{x_1-3x_3}{3})+f(\frac{3x_1+3x_3-x_2}{3})=f(x_1).$$ Moreover, we prove the generalized Hyers-Ulam -Rassias stability of homomorphisms in $C^*$-ternary algebras and of derivations on $C^*$-ternary algebras.