‎In this paper‎, ‎using fixed point method‎, ‎we prove the generalized Hyers-Ulam stability of‎ ‎random homomorphisms in random $C^*$-algebras and random Lie $C^*$-algebras‎ ‎and of derivations on Non-Archimedean random C$^*$-algebras and Non-Archimedean random Lie C$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...

In this paper, a link between the Hyers–Ulam stability and the Moore–Penrose inverse is established, that is, a closed operator has the Hyers–Ulam stability if and only if it has a bounded Moore–Penrose inverse. Meanwhile, the stability constant can be determined in terms of the Moore– Penrose inverse. Based on this result, some conditions for the perturbed operators having the Hyers– Ulam stab...

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...

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...