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Moradlou, Fridoun Korean Mathematical Society 2013 대한수학회논문집 Vol.28 No.2
Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces: $${\sum_{1{\leq}i_<j{\leq}n}}\;f(\frac{r_ix_i+r_jx_j}{k})=\frac{n-1}{k}{\sum_{i=1}^n}r_if(x_i)$$.
Moradlou, Fridoun,Rassias, Themistocles M. Korean Mathematical Society 2013 대한수학회보 Vol.50 No.6
In this paper, we investigate the generalized HyersUlam-Rassias stability of the following additive functional equation $$2\sum_{j=1}^{n}f(\frac{x_j}{2}+\sum_{i=1,i{\neq}j}^{n}\;x_i)+\sum_{j=1}^{n}f(x_j)=2nf(\sum_{j=1}^{n}x_j)$$, in quasi-${\beta}$-normed spaces.
Fridoun Moradlou,Themistocles M. Rassias 대한수학회 2013 대한수학회보 Vol.50 No.6
In this paper, we investigate the generalized HyersUlam– Rassias stability of the following additive functional equation [수식] in quasi-β-normed spaces.
WEAK CONVERGENCE THEOREMS FOR 2-GENERALIZED HYBRID MAPPINGS AND EQUILIBRIUM PROBLEMS
Alizadeh, Sattar,Moradlou, Fridoun Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.4
In this paper, we propose a new modied Ishikawa iteration for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of 2-generalized hybrid mappings in a Hilbert space. Our results generalize and improve some existing results in the literature. A numerical example is given to illustrate the usability of our results.
STABILITY OF A MIXED QUADRATIC AND ADDITIVE FUNCTIONAL EQUATION IN QUASI-BANACH SPACES
Najati, Abbas,Moradlou, Fridoun The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper we establish the general solution of the functional equation f(2x+y)+f(x-2y)=2f(x+y)+2f(x-y)+f(-x)+f(-y) and investigate the Hyers-Ulam-Rassias stability of this equation in quasi-Banach spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
STABILITY OF A QUADRATIC FUNCTIONAL EQUATION IN QUASI-BANACH SPACES
Najati, Abbas,Moradlou, Fridoun Korean Mathematical Society 2008 대한수학회보 Vol.45 No.3
In this paper we establish the general solution and investigate the Hyers-Ulam-Rassias stability of the following functional equation in quasi-Banach spaces. $${\sum\limits_{{{1{\leq}i<j{\leq}4}\limits_{1{\leq}k<l{\leq}4}}\limits_{k,l{\in}I_{ij}}}\;f(x_i+x_j-x_k-x_l)=2\;\sum\limits_{1{\leq}i<j{\leq}4}}\;f(x_i-x_j)$$ where $I_{ij}$={1, 2, 3, 4}\backslash${i, j} for all $1{\leq}i<j{\leq}4$. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc.
Stability of a mixed quadratic and additive functional equation in quasi-Banach spaces
Abbas Najati,Fridoun Moradlou 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper we establish the general solution of the functional equation f(2x + y) + f(x − 2y) = 2f(x + y) + 2f(x− y) + f(−x) + f(−y) and investigate the Hyers–Ulam–Rassias stability of this equation in quasi- Banach spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300. In this paper we establish the general solution of the functional equation f(2x + y) + f(x − 2y) = 2f(x + y) + 2f(x− y) + f(−x) + f(−y) and investigate the Hyers–Ulam–Rassias stability of this equation in quasi- Banach spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.
Stability of a quadratic functional equation in quasi--Banach spaces
Abbas Najati,Fridoun Moradlou 대한수학회 2008 대한수학회보 Vol.45 No.3
In this paper we establish the general solution and investigate the Hyers–Ulam–Rassias stability of the following functional equation in quasi-Banach spaces. [수식] where Iij = {1, 2, 3, 4}\{i, j} for all 1 ≤ i < j ≤ 4. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300. In this paper we establish the general solution and investigate the Hyers–Ulam–Rassias stability of the following functional equation in quasi-Banach spaces. [수식] where Iij = {1, 2, 3, 4}\{i, j} for all 1 ≤ i < j ≤ 4. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.
Additive Functional Inequalities in Banach Modules
Park, Choonkil,An, Jong Su,Moradlou, Fridoun Hindawi Publishing Corporation 2008 Journal of inequalities and applications Vol.2008 No.1
<P>We investigate the following functional inequality ‖2f(x)+2f(y)+2f(z)-f(x+y)-f(y+z)‖≤‖f(x+z)‖ in Banach modules over a C∗-algebra and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a C∗-algebra in the spirit of the Th. M. Rassias stability approach. Moreover, these results are applied to investigate homomorphisms in complex Banach algebras and prove the generalized Hyers-Ulam stability of homomorphisms in complex Banach algebras.</P>