Nonlinear stability of \(\rho\)-functional equations in latticetic random Banach lattice spaces
type: Item
instance of: scholarly article
title: Nonlinear stability of \(\rho\)-functional equations in latticetic random Banach lattice spaces
zbMATH Open document ID: 1434.39026
author: Mohammad Maleki V.
author: Reza Saadati
author: S. M. Vaezpour
published in: Mathematics
publication date: 2018-08-13T00:00:00Z
review text: Summary: In this paper, we prove the generalized nonlinear stability of the first and second of the following \(\rho\)-functional equations, \[ G(| a| \Delta_{\mathcal A}^\ast| b|) \Delta_{\mathcal B}^\ast G(| a|\Delta_{\mathcal A}^{\ast\ast}| b|) - G(| a|) \Delta_{\mathcal B}^{\ast\ast} G(| b|) = \rho (2 \left[G\left(\frac{| a| \Delta_{\mathcal A}^\ast| b |}{2}\right) \Delta_{\mathcal B}^\ast G \left(\frac{| a| \Delta_{\mathcal A}^{\ast\ast}| b|}{2}\right)\right] - G(| a|) \Delta_{\mathcal B}^{\ast\ast} G(| b|)), \] and \[ 2 \left [G \left(\frac{| a|\Delta_{\mathcal A}^\ast| b|}{2}\right)\Delta_{\mathcal B}^\ast G \left(\frac{| a|\Delta_{\mathcal A}^{\ast\ast}| b|}{2}\right)\right]-G(| a|) \Delta_{\mathcal B}^{\ast\ast} G(| b|) = \rho \left(G(| a| \Delta_{\mathcal A}^\ast | b |)\Delta_{\mathcal B}^\ast G(| a|\Delta_{\mathcal A}^{\ast\ast}| b|)-G(| a |)\Delta_{\mathcal B}^{\ast\ast}G (| b|)\right) \] in latticetic random Banach lattice spaces, where \(\rho\) is a fixed real or complex number with \(\rho \neq 1\).
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 6916896
zbMATH Keywords: stability
zbMATH Keywords: fixed point
zbMATH Keywords: lattictic random Banach space
zbMATH Keywords: \(\rho\)-functional equations
MaRDI profile type: Publication
full work available at URL: math6020022
OpenAlex ID: W2791248184
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DOI: 10.3390/MATH6020022
description: scientific article; zbMATH DE number 6916896