# Nonlinear Stability of ρ-Functional Equations in Latticetic Random Banach Lattice Spaces

^{1}

Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran 15875-4413, Iran

^{2}

Department of Mathematics, Iran University of Science and Technology, Tehran 15875-4413, Iran

^{*}

Author to whom correspondence should be addressed.

^{†}

Current address: Department of Mechanical Engineering, Amirkabir University of Technology, 424 Hafez Ave, Tehran 15875-4413, Iran.

Received: 27 December 2017 / Revised: 5 February 2018 / Accepted: 6 February 2018 / Published: 9 February 2018

(This article belongs to the Special Issue Stability Problems)

In this paper, we prove the generalized nonlinear stability of the first and second of the following $\rho $ -functional equations, $G\left(\right|a|{\Delta}_{\mathcal{A}}^{*}\left|b\right|){\Delta}_{\mathcal{B}}^{*}G\left(\right|a|{\Delta}_{\mathcal{A}}^{**}\left|b\right|)-G\left(\right|a\left|\right){\Delta}_{\mathcal{B}}^{**}G\left(\right|b\left|\right)=\rho (2\left[G,\left({\displaystyle \frac{\left|a\right|{\Delta}_{\mathcal{A}}^{*}\left|b\right|}{2}}\right),{\Delta}_{\mathcal{B}}^{*},G,\left({\displaystyle \frac{\left|a\right|{\Delta}_{\mathcal{A}}^{**}\left|b\right|}{2}}\right)\right]-G\left(\right|a\left|\right){\Delta}_{\mathcal{B}}^{**}G\left(\right|b\left|\right))$ , and $2\left[G,\left({\displaystyle \frac{\left|a\right|{\Delta}_{\mathcal{A}}^{*}\left|b\right|}{2}}\right),{\Delta}_{\mathcal{B}}^{*},G,\left({\displaystyle \frac{\left|a\right|{\Delta}_{\mathcal{A}}^{**}\left|b\right|}{2}}\right)\right]-G\left(\right|a\left|\right){\Delta}_{\mathcal{B}}^{**}G\left(\right|b\left|\right)=\rho \left(G\left(\right|a|,{\Delta}_{\mathcal{A}}^{*},\left|b\right|),{\Delta}_{\mathcal{B}}^{*},G\left(\right|a|,{\Delta}_{\mathcal{A}}^{**},\left|b\right|),-,G,\left(\right|a\left|\right),{\Delta}_{\mathcal{B}}^{**},G,\left(\right|b\left|\right)\right)$ in latticetic random Banach lattice spaces, where $\rho $ is a fixed real or complex number with $\rho \ne 1$ .
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**MDPI and ACS Style**

Maleki V., M.; Vaezpour, S.M.; Saadati, R. Nonlinear Stability of *ρ*-Functional Equations in Latticetic Random Banach Lattice Spaces. *Mathematics* **2018**, *6*, 22.

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