scholarly journals Best approximation of $(\mathcal{G}_{1},\mathcal{G}_{2})$-random operator inequality in matrix Menger Banach algebras with application of stochastic Mittag-Leffler and $\mathbb{H}$-Fox control functions

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Safoura Rezaei Aderyani ◽  
Reza Saadati ◽  
Themistocles M. Rassias ◽  
Choonkil Park
Keyword(s):  
Fixed Point ◽  
Best Approximation ◽  
Stochastic Matrix ◽  
Banach Algebras ◽  
Random Operator ◽  
Operator Inequality ◽  
Control Functions ◽  
Fixed Point Methods ◽  
Matrix Control ◽  
Fox Control

AbstractWe stabilize pseudostochastic $(\mathcal{G}_{1},\mathcal{G}_{2})$ ( G 1 , G 2 ) -random operator inequality using a class of stochastic matrix control functions in matrix Menger Banach algebras. We get an approximation for stochastic $(\mathcal{G}_{1},\mathcal{G}_{2})$ ( G 1 , G 2 ) -random operator inequality by means of both direct and fixed point methods. As an application, we apply both stochastic Mittag-Leffler and $\mathbb{H}$ H -fox control functions to get a better approximation in a random operator inequality.

scholarly journals Best approximation of κ-random operator inequalities in matrix MB-algebras

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Masoumeh Madadi ◽  
Donal O’Regan ◽  
Themistocles M. Rassias ◽  
Reza Saadati
Keyword(s):  
Best Approximation ◽  
Stochastic Matrix ◽  
Maximum Error ◽  
Random Operator ◽  
Operator Inequalities ◽  
Control Functions ◽  
Matrix Control

AbstractWe introduce a class of stochastic matrix control functions and apply them to stabilize pseudo stochastic κ-random operator inequalities in matrix MB-algebras. We obtain an approximation for stochastic κ-random operator inequalities and calculate the maximum error of the estimate.

scholarly journals Best approximation of a nonlinear fractional Volterra integro-differential equation in matrix MB-space

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Reza Chaharpashlou ◽  
Reza Saadati
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fractional Derivative ◽  
Stochastic Matrix ◽  
Fixed Point Method ◽  
Hilfer Fractional Derivative ◽  
Integro Differential Equation ◽  
Control Functions ◽  
Matrix Control ◽  
Rassias Stability

AbstractIn this article, we introduce a class of stochastic matrix control functions to stabilize a nonlinear fractional Volterra integro-differential equation with Ψ-Hilfer fractional derivative. Next, using the fixed-point method, we study the Ulam–Hyers and Ulam–Hyers–Rassias stability of the nonlinear fractional Volterra integro-differential equation in matrix MB-space.

ON APPROXIMATE n-ARY DERIVATIONS

2011 ◽  
Vol 08 (03) ◽  
pp. 485-500 ◽  
Author(s):  
M. ESHAGHI GORDJI ◽  
R. KHODABAKHSH ◽  
H. KHODAEI
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Algebras ◽  
C Algebras ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
Ternary Algebras ◽  
Fixed Point Methods ◽  
The Stability

C. Park et al. proved the stability of homomorphisms and derivations in Banach algebras, Banach ternary algebras, C*-algebras, Lie C*-algebras and C*-ternary algebras. In this paper, we improve and generalize some results concerning derivations. We first introduce the following generalized Jensen functional equation [Formula: see text] and using fixed point methods, we prove the stability of n-ary derivations and n-ary Jordan derivations in n-ary Banach algebras. Secondly, we study this functional equation with *-n-ary derivations in C*-n-ary algebras.

scholarly journals General solution and generalized Ulam-Hyers stability of a generalized n- type additive quadratic functional equation in Banach space and Banach algebra: direct and fixed point methods

2015 ◽  
Vol 3 (1) ◽  
pp. 25
Author(s):  
S. Murthy ◽  
M. Arunkumar ◽  
V. Govindan
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Fixed Point ◽  
Positive Integer ◽  
General Solution ◽  
Banach Algebra ◽  
Banach Algebras ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Fixed Point Methods

<p>In this paper, the authors introduce and investigate the general solution and generalized Ulam-Hyers stability of a generalized <em>n</em>-type additive-quadratic functional equation.</p><p><br />g(x + 2y; u + 2v) + g(x 􀀀 2y; u 􀀀 2v) = 4[g(x + y; u + v) + g(x 􀀀 y; u 􀀀 v)] 􀀀 6g(x; u)<br />+ g(2y; 2v) + g(􀀀2y;􀀀2v) 􀀀 4g(y; v) 􀀀 4g(􀀀y;􀀀v)</p><p>Where  is a positive integer with , in Banach Space and Banach Algebras using direct and fixed point methods.</p>

scholarly journals Stability and Superstability of Ring Homomorphisms on Non-Archimedean Banach Algebras

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
Z. Alizadeh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Algebras ◽  
Ulam Stability ◽  
Ring Homomorphisms ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
Fixed Point Methods

Using fixed point methods, we prove the superstability and generalized Hyers-Ulam stability of ring homomorphisms on non-Archimedean Banach algebras. Moreover, we investigate the superstability of ring homomorphisms in non-Archimedean Banach algebras associated with the Jensen functional equation.

Random iterative algorithms and almost sure stability in Banach spaces

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3611-3626 ◽  
Author(s):  
Abdul Khan ◽  
Vivek Kumar ◽  
Satish Narwal ◽  
Renu Chugh
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Iterative Algorithms ◽  
Random Operator ◽  
Almost Sure Stability ◽  
Random Fixed Point ◽  
Stochastic Version ◽  
Contractive Type ◽  
Bochner Integrability ◽  
Weakly Contractive

Many popular iterative algorithms have been used to approximate fixed point of contractive type operators. We define the concept of generalized ?-weakly contractive random operator T on a separable Banach space and establish Bochner integrability of random fixed point and almost sure stability of T with respect to several random Kirk type algorithms. Examples are included to support new results and show their validity. Our work generalizes, improves and provides stochastic version of several earlier results by a number of researchers.

Solvability of a 2 x 2 block operator matrix of chandrasekhar type on a Bananch algebra

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5169-5175 ◽  
Author(s):  
H.H.G. Hashem
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Of Solutions ◽  
Banach Algebras ◽  
Operator Matrix ◽  
Nonlinear Operators ◽  
Block Operator Matrix ◽  
Block Operator ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

In this paper, we study the existence of solutions for a system of quadratic integral equations of Chandrasekhar type by applying fixed point theorem of a 2 x 2 block operator matrix defined on a nonempty bounded closed convex subsets of Banach algebras where the entries are nonlinear operators.

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