ADDITIVE rho-FUNCTIONAL INEQUALITIES IN NON-ARCHIMEDEAN NORMED SPACES
By Choonkill Park. 2015
51 citations recorded by the source corpus.
In this paper, we solve the additive ρ -functional inequalities ‖ f (x+ y)− f (x)− f (y)‖ ∥∥∥ρ ( 2 f ( x+ y 2 ) − f (x)− f (y) ∥∥∥ (0.1) and ∥∥∥2 f ( x+ y 2 ) − f (x)− f (y) ∥∥∥ ‖ρ ( f (x+ y)− f (x)− f (y))‖ , (0.2) where ρ is a fixed non-Archimedean number with |ρ| < 1 . Furthermore, we prove the Hyers-Ulam stability of the additive ρ -functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces and prove the Hyers-Ulam stability of additive ρ -functional equations associated with the additive ρ -functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a225ae5e64cf510885e590fb61189cf5c0bed184
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Additive functional equations and partial multipliers in $$C^*$$C∗-algebras (2018, background): “Park [18,19] defined additive ρ-functional inequalities and proved the Hyers–Ulam stability of the additive ρ-functional inequalities in Banach spaces and non-Archimedean Banach spaces.”