in this paper, we investigate the generalizedhyers--ulam stability of the functional equation

In this work, by considering a class of matrix valued fuzzy controllers and using (?,?)-Cauchy–Jensen additive functional equation ((?,?)-CJAFE), we apply the Radu–Mihet method (RMM), which is derived from an alternative fixed point theorem, obtain existence unique solution H–U–R stability (Hyers–Ulam–Rassias) for homomorphisms Jordan on Lie algebras with ? members (?-LMVFA). With regards to ea...

and Applied Analysis 3 Theorem 2.2. A mapping f : X ×X → Y satisfies 1.1 if and only if it satisfies 1.2 . Proof. If f satisfies 1.1 , then we get

Let R be the set of positive real numbers, B a Banach space, f : R → B, and > 0, p, q, P,Q ∈ R with pqPQ/ 0. We prove the Hyers-Ulam stability of the Jensen type logarithmic functional inequality ‖f xy − Pf x − Qf y ‖ ≤ in restricted domains of the form { x, y : x > 0, y > 0, xy ≥ d} for fixed k, s ∈ R with k / 0 or s / 0 and d > 0. As consequences of the results we obtain asymptotic behaviors ...

‎hensel [k‎. ‎hensel‎, ‎deutsch‎. ‎math‎. ‎verein‎, ‎{6} (1897), ‎83-88.] discovered the $p$-adic number as a‎ ‎number theoretical analogue of power series in complex analysis‎. ‎fix ‎a prime number $p$‎. ‎for any nonzero rational number $x$‎, ‎there‎ ‎exists a unique integer $n_x inmathbb{z}$ such that $x = ‎frac{a}{b}p^{n_x}$‎, ‎where $a$ and $b$ are integers not divisible by ‎$p$‎. ‎then $|x...