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PRIME IDEALS IN LIPSCHITZ ALGEBRAS OF FINITE DIFFERENTIABLE FUNCTIONS
Ebadian, Ali 호남수학회 2000 호남수학학술지 Vol.22 No.1
Lipschitz Algebras Lip(X,α) and lip(X,α) were first studied by D. R. Sherbert in 1964. B. Pavlovic in 1995 shown that in these algebras, the prime ideals containing a given prime ideal form a chain. Tn this paper, we show that the above property holds in Lip^n(X,α) and lip^n(X,α), the Lipschitz algebras of finite differentiable functions on a perfect compact place set X.
Ebadian, Ali Department of Mathematics 2013 Kyungpook mathematical journal Vol.53 No.2
Let $\mathcal{A}$ be a Banach ternary algebra over a scalar field R or C and $\mathcal{X}$ be a ternary Banach $\mathcal{A}$-module. A quartic mapping $D\;:\;(\mathcal{A},[\;]_{\mathcal{A}}){\rightarrow}(\mathcal{X},[\;]_{\mathcal{X}})$ is called a $4^{th}$- order ternary derivation if $D([x,y,z])=[D(x),y^4,z^4]+[x^4,D(y),z^4]+[x^4,y^4,D(z)]$ for all $x,y,z{\in}\mathcal{A}$. In this paper, we prove Ulam stability generalizations of $4^{th}$- order ternary derivations associated to the following JMRassias quartic functional equation on fr$\acute{e}$che algebras: $$f(kx+y)+f(kx-y)=k^2[f(x+y)+f(x-y)]+2k^2(k^2-1)f(x)-2(k^2-1)f(y)$$.
Ebadian, Ali,Aghalary, Rasoul,Najafzadeh, Shahram Department of Mathematics 2010 Kyungpook mathematical journal Vol.50 No.4
A new class of univalent holomorphic functions with fixed finitely many coefficients based on Generalized fractional derivative are introduced. Also some important properties of this class such as coefficient bounds, convex combination, extreme points, Radii of starlikeness and convexity are investigated.
SOME EXTENSION RESULTS CONCERNING ANALYTIC AND MEROMORPHIC MULTIVALENT FUNCTIONS
Ebadian, Ali,Masih, Vali Soltani,Najafzadeh, Shahram Korean Mathematical Society 2019 대한수학회보 Vol.56 No.4
Let $\mathscr{B}^{{\eta},{\mu}}_{p,n}\;({\alpha});\;({\eta},{\mu}{\in}{\mathbb{R}},\;n,\;p{\in}{\mathbb{N}})$ denote all functions f class in the unit disk ${\mathbb{U}}$ as $f(z)=z^p+\sum_{k=n+p}^{\infty}a_kz^k$ which satisfy: $$\|\[{\frac{f^{\prime}(z)}{pz^{p-1}}}\]^{\eta}\;\[\frac{z^p}{f(z)}\]^{\mu}-1\| <1-{\frac{\alpha}{p}};\;(z{\in}{\mathbb{U}},\;0{\leq}{\alpha}<p)$$. And $\mathscr{M}^{{\eta},{\mu}}_{p,n}\;({\alpha})$ indicates all meromorphic functions h in the punctured unit disk $\mathbb{U}^*$ as $h(z)=z^{-p}+\sum_{k=n-p}^{\infty}b_kz^k$ which satisfy: $$\|\[{\frac{h^{\prime}(z)}{-pz^{-p-1}}}\]^{\eta}\;\[\frac{1}{z^ph(z)}\]^{\mu}-1\|<1-{\frac{\alpha}{p}};\;(z{\in}{\mathbb{U}},\;0{\leq}{\alpha}<p)$$. In this paper several sufficient conditions for some classes of functions are investigated. The authors apply Jack's Lemma, to obtain this conditions. Furthermore, sufficient conditions for strongly starlike and convex p-valent functions of order ${\gamma}$ and type ${\beta}$, are also considered.
Some extension results concerning analytic and meromorphic multivalent functions
Ali Ebadian,Vali Soltani Masih,Shahram Najafzadeh 대한수학회 2019 대한수학회보 Vol.56 No.4
Let $\mathscr{B}_{p,n}^{\upeta, \upmu}\left(\upalpha\right)$; $\left( \upeta, \upmu\in \mathbb{R}, n,p\in \mathbb{N}\right) $ denote all functions $f$ class in the unit disk $\mathbb{U}$ as $f(z)=z^p+\sum_{k=n+p}^{\infty}a_kz^k$ which satisfy: \begin{align*} & \left| \left[ \frac{f'(z)}{pz^{p-1}}\right]^{\upeta} \left[ \frac{z^p}{f(z)}\right] ^{\upmu}-1\right| <1-\frac{\upalpha}{p}; \quad \left( z\in \mathbb{U}, \: 0\leq \upalpha<p\right). \intertext{ And $\mathscr{M}_{p,n}^{\upeta,\upmu}\left(\upalpha\right)$ indicates all meromorphic functions $h$ in the punctured unit disk $\mathbb{U}^{\ast}$ as $h(z)=z^{-p}+\sum_{k=n-p}^{\infty}b_kz^k$ which satisfy:} & \left| \left[ \frac{h'(z)}{-pz^{-p-1}}\right]^{\upeta} \left[ \frac{1}{z^p h(z)}\right]^{\upmu}-1\right| <1-\frac{\upalpha}{p}; \quad \left( z\in \mathbb{U}, \: 0\leq \upalpha<p\right). \end{align*} In this paper several sufficient conditions for some classes of functions are investigated. The authors apply Jack's Lemma, to obtain this conditions. Furthermore, sufficient conditions for strongly starlike and convex $p$-valent functions of order $\gamma$ and type $\beta$, are also considered.
PSEUDO JORDAN HOMOMORPHISMS AND DERIVATIONS ON MODULE EXTENSIONS AND TRIANGULAR BANACH ALGEBRAS
( Ali Ebadian ),( Fariba Farajpour ),( Shahram Najafzadeh ) 호남수학회 2021 호남수학학술지 Vol.43 No.1
This paper considers pseudo Jordan homomorphisms on module extensions of Banach algebras and triangular Banach algebras. We characterize pseudo Jordan homomorphisms on module extensions of Banach algebras and triangular Banach algebras. Moreover, we define pseudo derivations on the above stated Banach algebras and characterize this new notion on those algebras.
PSEUDO n-JORDAN HOMOMORPHISMS AND PSEUDO n-HOMOMORPHISMS ON BANACH ALGEBRAS
Ebadian, Ali,Gordji, Madjid Eshaghi,Jabbari, Ali The Honam Mathematical Society 2020 호남수학학술지 Vol.42 No.2
In this paper, we correct some errors and typos of [2] and introduce a new concept related to pseudo n-Jordan homomorphisms, that we call it pseudo n-homomorphism. We investigate automatic continuity and positivity of pseudo n-homomorphisms and pseudo n-Jordan homomorphisms on Banach algebras and C*-algebras. Moreover, we show that the sum of two pseudo n-Jordan homomorphisms is not a pseudo n-Jordan homomorphism and we show that under some conditions the sum of two pseudo n-Jordan homomorphisms is a pseudo n-Jordan homomorphism.
The Maximal Ideal Space of Extended Differentiable Lipschitz Algebras
Abolfathi, Mohammad Ali,Ebadian, Ali Department of Mathematics 2020 Kyungpook mathematical journal Vol.60 No.1
In this paper, we first introduce new classes of Lipschitz algebras of infinitely differentiable functions which are extensions of the standard Lipschitz algebras of infinitely differentiable functions. Then we determine the maximal ideal space of these extended algebras. Finally, we show that if X and K are uniformly regular subsets in the complex plane, then R(X, K) is natural.
T-NEIGHBORHOODS IN VARIOUS CLASSES OF ANALYTIC FUNCTIONS
Shams, Saeid,Ebadian, Ali,Sayadiazar, Mahta,Sokol, Janusz Korean Mathematical Society 2014 대한수학회보 Vol.51 No.3
Let $\mathcal{A}$ be the class of analytic functions f in the open unit disk $\mathbb{U}$={z : ${\mid}z{\mid}$ < 1} with the normalization conditions $f(0)=f^{\prime}(0)-1=0$. If $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ and ${\delta}$ > 0 are given, then the $T_{\delta}$-neighborhood of the function f is defined as $$TN_{\delta}(f)\{g(z)=z+\sum_{n=2}^{\infty}b_nz^n{\in}\mathcal{A}:\sum_{n=2}^{\infty}T_n{\mid}a_n-b_n{\mid}{\leq}{\delta}\}$$, where $T=\{T_n\}_{n=2}^{\infty}$ is a sequence of positive numbers. In the present paper we investigate some problems concerning $T_{\delta}$-neighborhoods of function in various classes of analytic functions with $T=\{2^{-n}/n^2\}_{n=2}^{\infty}$. We also find bounds for $^{\delta}^*_T(A,B)$ defined by $$^{\delta}^*_T(A,B)=jnf\{{\delta}>0:B{\subset}TN_{\delta}(f)\;for\;all\;f{\in}A\}$$ where A, B are given subsets of $\mathcal{A}$.