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Mathematics 2018, 6(2), 22; https://doi.org/10.3390/math6020022

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
Current address: Department of Mechanical Engineering, Amirkabir University of Technology, 424 Hafez Ave, Tehran 15875-4413, Iran.
*
Author to whom correspondence should be addressed.
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)
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Abstract

In this paper, we prove the generalized nonlinear stability of the first and second of the following ρ -functional equations, G ( | a | Δ A * | b | ) Δ B * G ( | a | Δ A * * | b | ) G ( | a | ) Δ B * * G ( | b | ) = ρ ( 2 G | a | Δ A * | b | 2 Δ B * G | a | Δ A * * | b | 2 G ( | a | ) Δ B * * G ( | b | ) ) , and 2 G | a | Δ A * | b | 2 Δ B * G | a | Δ A * * | b | 2 G ( | a | ) Δ B * * G ( | b | ) = ρ G ( | a | Δ A * | b | ) Δ B * G ( | a | Δ A * * | b | ) G ( | a | ) Δ B * * G ( | b | ) in latticetic random Banach lattice spaces, where ρ is a fixed real or complex number with ρ 1 . View Full-Text
Keywords: stability; fixed point; lattictic random Banach space; ρ-functional equations stability; fixed point; lattictic random Banach space; ρ-functional equations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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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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