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May 6, 2026Demonstratio MathematicaOpen Access

Generalized Hyers–Ulam stability of mixed-type additive-quartic mappings in 2-Banach spaces

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Authors

ASArumugam Ponmana SelvanMOMasakazu OnitsukaVLVelu Lakshmi

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Overview

Demonstrates Hyers-Ulam stability in 2-Banach spaces for mixed-type additive-quartic functional equations, indicating functional inequalities dictate close approximations of solutions.

Key Points

  • To explore the stability of mixed-type additive-quartic functional equations in 2-Banach spaces using the direct method.
  • Categorization of mappings into odd, even, and general categories.
  • Exploration of functional inequalities related to each category of mappings.
  • Analysis of the approximation of solutions for each mapped type.
  • Established generalized Hyers-Ulam stability for odd mappings where exact and approximate solutions are close.
  • Showed that even mappings maintain closeness between exact quartic solutions and approximate solutions.
  • Demonstrated that general mappings, comprising both additive and quartic components, closely approximate the exact solutions.

Cite This Study

Selvan et al. (2026) studied this question.

synapsesocial.com/papers/69fa989404f884e66b53245chttps://doi.org/10.1515/dema-2025-0237
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Hyers–Ulam Stability of a Multi-Variable Additive-Quadratic Functional Equation2026 · 1 citations
  2. 2Approximation on a system of equations driving from mixed type additive and quartic functional equations2026
  3. 3The system of mixed type additive-quadratic equations and approximations2024 · 1 citations
  4. 4Hyers–Ulam Stability of Mixed Quintic and Sextic Equations in Matrix‐Valued Non‐Archimedean Random Normed Spaces via Fixed Point Methods2026
  5. 5The Stability of Quadratic Mappings via the Semi-Parallelogram Law with Asymmetric Controls2026