This manuscript presents Hyers-Ulam stability and Hyers--Ulam--Rassias stability results of non-linear Volterra integro--delay dynamic system on time scales with fractional integrable impulses. Picard fixed point theorem  is used for obtaining  existence and uniqueness of solutions. By means of   abstract Gr"{o}nwall lemma, Gr"{o}nwall's inequality on time scales, we establish  Hyers-Ulam stabi...

In this paper,we consider functional equations involving a two variables examine some of these equations in greater detail and we study applications of cauchy’s equation.using the generalized hyers-ulam-rassias stability of quaradic functional equations finding the solution of two variables(quaradic functional equations) 1.INTRODUCTION We achieve the general solution and the generalized Hyers-U...

In 1940, Ulam [1] gave a wide ranging talk before the mathematics club of the University of Wisconsin in which he discussed a number of important unsolved problems. Among those was the question concerning the stability of group homomorphisms. Let G1 be a group and let G2 be a metric group with the metric d(·,·). Given ε > 0, does there exist a δ > 0 such that if a function h : G1 → G2 satisfies...

In this paper, we investigate four different types of Ulam stability, i.e., Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of nonlinear implicit fractional differential equations with non-instantaneous integral impulses and nonlinear integral boundary condition. We also establish certain conditions fo...

1. A. H. Sales, About K-Fibonacci numbers and their associated numbers; Int. J. of Math Forum, Vol. 6, no.50, (2011) 24732479. 2. D. H. Hyers, On the stability if linear functional equation, Proc. Natl. Acad. Sci. USA. 27(1941) 221-224. 3. D. H. Hyers, G. Isac and Th. M Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Boston, 1998. 4. D. H. Hyers and Th. M. Rassias, ...

In this paper we present four types of Ulam stability for ordinary differential equations: Ulam-Hyers stability, generalized UlamHyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-HyersRassias stability. Some examples and counterexamples are given.

and Applied Analysis 3 The functional equation 1.7 was first solved by Kannappan. In fact he proved that a mapping f on a real vector space is a solution of 1.7 if and only if there exists a symmetric biadditive mapping B and an additive mapping A such that f x B x, x A x , for any x see 9 . The stability problem for 1.7 is also studied in 26 . Moreover 1.7 was pexiderized and solved by Kannapp...

in the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{e}$$ isgiven where $sigma$ is an involution of the normed space $e$ and$k$ is a fixed positive integer. furthermore we investigate thehyers-ulam-rassias stability of the functional equation. thehyers-ulam stability on unbounded domains is also studied.applic...