We will apply a fixed point method for proving the Hyers–Ulam stability of the functional equation f(x+ y) = f(x)f(y) f(x)+f(y) .

Abstract The paradigm of choice practice represents the psychological theory learning in development moral judgment. It is concerned with evaluating implications several choices and selecting one them to implement. goal this work provide a generic functional equation observe behavior animals such circumstances. Our suggested can be employed describe well-known psychology theories. fixed point t...

In this paper, we obtain the general solution and the generalized   Hyers-Ulam-Rassias stability in random normed spaces, in non-Archimedean spaces and also in $p$-Banach spaces and finally the stability via fixed point method for a functional equationbegin{align*}&D_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1, i...

The Hyers-Ulam stability problems of functional equations go back to 1940 when S. M. Ulam proposed a question concerning the approximate homomorphisms from a group to a metric group see 1 . A partial answer was given by Hyers et al. 2, 3 under the assumption that the target space of the involved mappings is a Banach space. After the result of Hyers, Aoki 4 , and Bourgin 5, 6 dealt with this pro...

In this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-Archimedean number with $alpha^{-2}neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic $alpha$-functional equation (0.1) in non-Archimedean Banach spaces.

In this paper, we establish the generalized Hyers–Ulam–Rassias stability of C-ternary ring homomorphisms associated to the Trif functional equation d · C d−2f( x1 + · · ·+ xd d ) + C d−2 d ∑

In 1940 and 1964, Ulam proposed the general problem: “When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?”. In 1941, Hyers solved this stability problem for linear mappings. According to Gruber 1978 this kind of stability problems are of the particular interest in probability theory and in ...

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...

In this paper, we discuss several problems related to the neutral fractional Volterra-Fredholm integro-differential systems in Banach spaces. Existence of Schaefer's fixed point and Ulam-Hyers-Rassias stability properties for problem will be discussed. Some results are presented, under appropriate conditions, some open questions pointed out. Our extend recent given \(\psi\)-fractional derivative.

Differential equations with fractional derivative are being extensively used in the modelling of transmission many infective diseases like HIV, Ebola, and COVID-19. Analytical solutions unreachable for a wide range such kind equations. Stability theory sense Ulam is essential as it provides approximate analytical solutions. In this article, we utilize some fixed point theorem (FPT) to investiga...