Synapse
⌘+K
Synapse
PulseExploreClubsResearchersJournals
Instagram
HomeClubsExplore
August 8, 2026MathematicsOpen Access

The Stability of Quadratic Mappings via the Semi-Parallelogram Law with Asymmetric Controls

View Full Paper
Ask AI
Bookmark
Share

Authors

AAAdolfo Pimienta AcostaJCJohnny CuadroODOswaldo Dede

Discussion

Loading...

Member takes

Overview

Randomized trial investigates stability of quadratic mappings in metric spaces, suggesting implications for functional equations.

Key Points

  • This research aims to explore the Hyers–Ulam stability of quadratic mappings using the semi-parallelogram law.
  • Analyzed a three-variable functional equation under natural growth conditions on the error term.
  • Used the direct method and fixed point alternative in generalized metric spaces.
  • Examined the effects of asymmetric control functions and power-type perturbations.
  • Each solution uniquely splits into an additive and a quadratic mapping.
  • Stability estimates were established for p<2 with explicit constants, while at p=2, stability methods fail.
  • Demonstrated how the nature of perturbations affects stability through detailed examples.

Cite This Study

Acosta et al. (2026) studied this question.

synapsesocial.com/papers/6a76daaaf12abadc798151cehttps://doi.org/10.3390/math14152837
View Full Paper
Ask AI
Bookmark
Share