In this paper, the concept of stability for fuzzy control systems is discussed from a mathematical point of view. Our main objective is to investigate the stability of fuzzy Linear systems with bounded input and bounded output. Necessary and sufficient conditions for this kind of stability are presented by a theorem and it is illustrated by solving an example.

In this paper, we show the stability of Gustafson, Wei-dmann, Kato, Wolf, Schechter and Browder essential spectrum of bounded Linear operators on Banach spaces which remain invari-ant under additive perturbations belonging to a broad classes of operators U such that g(Um)<1 where g(.) is a measure of non-compactness.

In this paper some results about the Hyers-Ulam-Rassias stability for the Linear functional equations in general form and its Pexiderized can be proved for given functions on general domain to a complex Banach spaces under some suitable conditions. In connection with the problem of G. L. Forti in the 13st ICFEI we consider the common stability for the systems of functional equations and our aim is to establish some common Hyers-Ulam-Rassias stability for systems of homogeneous Linear functional equations. The results is applied to the study of some superstability results for the exponential functional equation.

In the present work we continue studying the solvability of the Linear functional equations åNj=1Cj F o aj=H and also the strong and weak stability of the corresponding operator P (see the definition below). By analogy with the Cauchy and Jensen operators once more model operator pˆis considered, and the stability problems as well as some solvability problems for pˆ are studied. Several unsolved problem of a general character are formulated.