Using the Hyers-Ulam-Rassias stability method, weinvestigate isomorphisms in Banach algebras and derivations onBanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}Moreover, we prove the Hyers-Ulam-Rassias stability of homomorphismsin Banach algebras and of derivations on Banach ...

The Hyers-Ulam stability, the Hyers-Ulam-Rassias stability, and also the stability in the spirit of Gǎvru̧ta for each of the following quadratic functional equations f(x+y)+ f(x−y) = 2f(x)+ 2f(y), f(x+y + z)+ f(x−y)+ f(y − z)+ f(z−x) = 3f(x)+3f(y)+3f(z), f (x+y+z)+f(x)+f(y)+f(z)= f(x+y)+f(y+z)+f(z+x) are investigated. 2000 Mathematics Subject Classification. Primary 39B52, 39B72, 39B82.

In 1940, Ulam [1] proposed the famous Ulam stability problem of linear mappings. In 1941, Hyers [2] considered the case of approximately additive mappings f : E→ E′, where E and E′ are Banach spaces and f satisfies Hyers inequality ‖ f (x+ y)− f (x)− f (y)‖ ≤ ε for all x, y ∈ E. It was shown that the limit L(x) = limn→∞ 2−n f (2nx) exists for all x ∈ E and that L : E→ E′ is the unique additive ...

This paper aims to study the existence and uniqueness of solution for nonlocal multiorder implicit differential equation involving Hilfer fractional derivative on unbounded domains a , ∞ ≥ 0 , in an applicable Banach...

Abstract In this research work, a class of multi-term fractional pantograph differential equations (FODEs) subject to antiperiodic boundary conditions (APBCs) is considered. The ensuing problem involves proportional type delay terms and constitutes subclass known as pantograph. On using fixed point theorems due Banach Schaefer, some sufficient are developed for the existence uniqueness solution...

This paper deals with the existence, uniqueness, and Ulam-stability outcomes for $\Xi$-Hilfer fractional fuzzy differential equations impulse. Further, by using techniques of nonlinear functional analysis, we study Ulam-Hyers-Rassias stability.

In this paper, we investigate homomorphisms between JB∗ -triples, and derivations on JB∗ -triples associated to the following Cauchy–Jensen type additive functional equation f ( x + y 2 + z ) + f ( x + z 2 + y ) + f ( y + z 2 + x ) = 2[f (x) + f (y) + f (z)]. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem that appeared in his paper: On the stabilit...

In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of the following Cauchy-Jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem t...

In this current paper, using q-fractional calculus, we study the Duffing–Rayleigh type problem with sequential fractional q-derivative of Caputo type. We investigate existence and uniqueness solutions by applying some classical fixed point theorems. Also define Ulam–Hyers Ulam–Hyers–Rassias stabilities for our problem. An example is presented to illustrate main results.

In this paper, we obtain sufficient conditions for Hyers–Ulam and Hyers–Ulam–Rassias stability of an abstract second–order nonlinear dynamic equation on bounded time scales. An illustrative example is given to show the applicability theoretical results.