arXiv subjects
Publications and source records attributed to John Michael Rassias.
This paper explores the Hyers-Ulam stability of generalized Jensen additive and quadratic functional equations in \(β\)-homogeneous \(F\)-space, showing that approximately satisfying mappings have a unique exact approximating counterpart within a specific bound.
We establish the best (minimum) constant for Ulam stability of first-order linear $h$-difference equations with a periodic coefficient. First, we show Ulam stability and find the Ulam stability constant for a first-order linear equation with a period-two coefficient, and give several examples. In the last section we prove Ulam stability for a periodic coefficient function of arbitrary finite period. Results on the associated first-order perturbed linear equation with periodic coefficient are also included.
This paper focuses at the various stability results of reciprocal-nonic and reciprocal-decic functional equations in non-Archimedes fields and illustrations of the proper examples for their non-stabilities.
In this paper, we proved the generalized Hyers-Ulam stability of homomorphisms in $C^*$- ternary algebras and of derivations on $C^*$-ternary algebras for the following Cauchy- Jensen functional equation $$3f\bigg(\frac{x+y+z}{3}\bigg)=2f\bigg(\frac{x+y}{2}\bigg)+f(z).$$ These were applied to investigate isomorphisms between $C^*$-ternary algebras.