scholarly journals A Fixed Point Approach to Superstability of Generalized Derivations on Non-Archimedean Banach Algebras

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
M. B. Ghaemi ◽  
Badrkhan Alizadeh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Banach Algebras ◽  
Generalized Derivations ◽  
Cauchy Functional Equation ◽  
Fixed Point Approach

We investigate the superstability of generalized derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchy functional equation.

scholarly journals Stability and Superstability of Generalized (, )-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
M. Eshaghi Gordji ◽  
M. B. Ghaemi ◽  
G. H. Kim ◽  
Badrkhan Alizadeh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Generalized Derivation ◽  
Additive Mapping ◽  
Generalized Derivations ◽  
Cauchy Functional Equation ◽  
Cauchy’S Functional Equation ◽  
Additive Cauchy Functional Equation

Let be an algebra, and let , be ring automorphisms of . An additive mapping is called a -derivation if for all . Moreover, an additive mapping is said to be a generalized -derivation if there exists a -derivation such that for all . In this paper, we investigate the superstability of generalized -derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchy’s functional equation.

scholarly journals Nearly Ternary Quadratic Higher Derivations on Non-Archimedean Ternary Banach Algebras: A Fixed Point Approach

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
M. B. Ghaemi ◽  
J. M. Rassias ◽  
Badrkhan Alizadeh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Banach Algebras ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Fixed Point Approach ◽  
Ternary Algebras ◽  
The Stability

We investigate the stability and superstability of ternary quadratic higher derivations in non-Archimedean ternary algebras by using a version of fixed point theorem via quadratic functional equation.

scholarly journals On Hyperstability of the Cauchy Functional Equation in n-Banach Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1886
Author(s):  
Janusz Brzdęk ◽  
El-sayed El-hady
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Main Tool ◽  
Normed Spaces ◽  
Cauchy Functional Equation ◽  
Additive Cauchy Functional Equation

We present some hyperstability results for the well-known additive Cauchy functional equation f(x+y)=f(x)+f(y) in n-normed spaces, which correspond to several analogous outcomes proved for some other spaces. The main tool is a recent fixed-point theorem.

scholarly journals Pentagonal Cone b-metric Spaces over Banach Algebras and Fixed Point Theorem of Generalized Lipschitz Mapping

2018 ◽  
Vol 22 ◽  
pp. 01003 ◽  
Author(s):  
Abba Auwalu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Lipschitz Mapping ◽  
Banach Fixed Point Theorem ◽  
Cone Metric ◽  
Generalized Lipschitz Mapping

In this paper, we introduce the concept of pentagonal cone b-metric space over Banach algebras as a generalization of cone metric space over Banach algebras and many of its generalizations. Furthermore, we prove Banach fixed point theorem in such a space. Our result unify, complement and/or generalized some recent results in the papers [1–7], and many others. We provide some examples to elucidate the validity and superiority of our results.

scholarly journals Existence of solutions for hybrid fractional pantograph equations

2015 ◽  
Vol 9 (1) ◽  
pp. 150-167 ◽  
Author(s):  
Mohamed Darwish ◽  
Kishin Sadarangani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Derivative ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Banach Algebras ◽  
Type Condition ◽  
Measures Of Noncompactness ◽  
Pantograph Equation ◽  
Liouville Fractional Derivative

In this paper, we study the existence of the hybrid fractional pantograph equation {D?0+[x(t)/f(t,x(t),x(?t))= g(t,x(t), x(?t)), 0 < t < 1, x(0) = 0, where ?,?,? ?((0,1) and D?0+ denotes the Riemann-Liouville fractional derivative. The results are obtained using the technique of measures of noncompactness in the Banach algebras and a fixed point theorem for the product of two operators verifying a Darbo type condition. Some examples are provided to illustrate our results.

A fixed point approach to local minimax theory

1986 ◽  
Vol 99 (2) ◽  
pp. 339-346
Author(s):  
W. J. R. Eplett
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Hypothesis Tests ◽  
Fixed Point Approach ◽  
Minimax Theory ◽  
Minimax Estimators

AbstractThe generalized Neyman-Pearson theorem for constructing robust hypothesis tests proved by Huber and Strassen is obtained here as an application of the Kakutani-Fan fixed point theorem. The same technique is applied to obtain the existence of locally minimax estimators.

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