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.

We study the approximate solution of special type \(n^{th}\) order linear differential equation by applying initial and boundary conditions using Taylor's series formula. That is, we prove sufficient condition for Mittag-Leffler-Hyers-Ulam stability Mittag-Leffler-Hyers-Ulam-Rassias higher with

In this article, we prove the generalized Hyers–Ulam stability of the following Cauchy additive functional equation

In 1994–1995, DIMACS sponsored a theme year on computational biology. Among the numerous seminars and workshops was one organized by Alberto Apostolico and Raffaele Giancarlo, recapitulated in their 1998 paper, on the history and motivations for sequence comparison. In my participation in this event, I was led to consider some of the early interactions, at the Centre de recherches mathématiques...

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...

We study the properties of the Google matrix of an Ulam network generated by intermittency maps. This network is created by the Ulam method which gives a matrix approximant for the Perron-Frobenius operator of dynamical map. The spectral properties of eigenvalues and eigenvectors of this matrix are analyzed. We show that the PageRank of the system is characterized by a power law decay with the ...

In this paper, we obtain the Hyers–Ulam–Rassias stability of the generalized Pexider functional equation ∑ k∈K f(x+ k · y) = |K|g(x) + |K|h(y), x, y ∈ G, where G is an abelian group, K is a finite abelian subgroup of the group of automorphism of G. The concept of Hyers–Ulam–Rassias stability originated from Th.M. Rassias’ Stability Theorem that appeared in his paper: On the stability of the lin...

* Correspondence: baak@hanyang. ac.kr Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea Full list of author information is available at the end of the article Abstract In this article, we prove the Hyers-Ulam stability of exact second-order linear differential equations. As a consequence, we show the Hyers-Ulam stability of the fo...

In this paper, we establish the Hyers–Ulam–Rassias stability of ring homomorphisms and ring derivations on fuzzy Banach algebras.

(Joint work with Alexandru Chirvasitu.) The Borsuk-Ulam theorem in algebraic topology indicates restrictions for equivariant maps between spheres; in particular, there is no odd map from a sphere to another sphere of lower dimension. This idea may be generalized greatly in both the topological and operator algebraic settings for actions of compact (quantum) groups, leading to the the noncommuta...