Hyers–Ulam stability of norm-additive functional equations via $(\delta , \epsilon )$-isometries
Copyright policy )Hyers–Ulam stability of norm-additive functional equations via $(\delta , \epsilon )$-isometries
Abstract This research examines the Hyers–Ulam stability of norm-additive functional equations expressed as ∥ ξ ( g h − 1 ) ∥ = ∥ ξ ( g ) − ξ ( h ) ∥ , ∥ ξ ( g h ) ∥ = ∥ ξ ( g ) + ξ ( h ) ∥ , $$\begin{aligned}& \|\xi (gh^{-1})\|=\|\xi (g)-\xi (h)\|,\\& \|\xi (gh)\|=\|\xi (g)+\xi (h)\|, \end{aligned}$$ through the utilization of ( δ , ϵ ) $(\delta , \epsilon )$ -isometries. In this context, ξ : G → X $\xi : G \to X$ represents a surjective (δ-surjective) mapping, where G denotes noncommutative group (arbitrary group) and X signifies a Banach space (or a real Banach space).
- Xinxiang University China (People's Republic of)
- Xinjiang University China (People's Republic of)
- Sun Yat-sen University China (People's Republic of)
- Minjiang University China (People's Republic of)
Hyers–Ulam stability, Banach space, Perturbations of functional-differential equations, Functional analysis techniques applied to functions of several complex variables, isometry, QA1-939, norm-additive functional equations, Functional equations for functions with more general domains and/or ranges, Stability, separation, extension, and related topics for functional equations, Hyers-Ulam stability, Isometry, Norm-additive functional equations, Mathematics
Hyers–Ulam stability, Banach space, Perturbations of functional-differential equations, Functional analysis techniques applied to functions of several complex variables, isometry, QA1-939, norm-additive functional equations, Functional equations for functions with more general domains and/or ranges, Stability, separation, extension, and related topics for functional equations, Hyers-Ulam stability, Isometry, Norm-additive functional equations, Mathematics
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