Hyers-Ulam-Rassias stability of functional equations with parameters
Jing Zhang, Qi Liu, Yongmo Hu, Linlin Fu, Yuxin Wang, Jinyu Xia, John Michael Rassias, Choonkil Park, Yongjin Li
TL;DR
This paper investigates the Hyers-Ulam stability of generalized Jensen additive and quadratic functional equations in ta-homogeneous F-spaces, demonstrating that approximate solutions are close to unique exact solutions within a certain bound.
Contribution
It extends the Hyers-Ulam stability theory to generalized Jensen and quadratic equations in ta-homogeneous F-spaces, providing new stability results.
Findings
Approximately satisfying mappings have unique exact solutions nearby.
Stability bounds are established for solutions in ta-homogeneous F-spaces.
The results generalize previous stability theorems to broader functional equations.
Abstract
This paper explores the Hyers-Ulam stability of generalized Jensen additive and quadratic functional equations in \(\beta\)-homogeneous \(F\)-space, showing that approximately satisfying mappings have a unique exact approximating counterpart within a specific bound.
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