Ulam-Hyers stability of dynamic equations on time scales via Picard operators

Hyers-Ulam Stability of Non-Linear Volterra Integro-Delay Dynamic System with Fractional Integrable Impulses on Time Scales

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...

Ulam-hyers Stability of Fixed Point Equations for Multivalued Operators on Kst Spaces

In this paper we define the notions of Ulam-Hyers stability on KST spaces and cwweakly Picard operator for the multivalued operators case in order to establish a relation between these.

Ulam stabilities for nonlinear Volterra-Fredholm delay integrodifferential equations

In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of ob...

Hyers-Ulam Stability of Weighted Composition Operators on L^p-Spaces

Ulam-Hyers stability of elliptic partial differential equations in Sobolev spaces

In the present paper we study the Ulam-Hyers stability of some elliptic partial differential equations on bounded domains with Lipschitz boundary. We use direct techniques and also some abstract methods of Picard operators. The novelty of our approach consists in the fact that we are working in Sobolev spaces and we do not need to know the explicit solutions of the problems or the Green functio...