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

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 .

Keywords

• stability
• fixed point
• lattictic random Banach space
• ρ-functional equations