Abstract— In this paper, we present an algorithmic approach to the construction of Lyapunov functions for infinitedimensional systems. This paper unifies and extends many previous results which have appeared in conference and journal format. The unifying principle is that a linear matrix parametrization of operators in Hilbert space inevitably leads to a linear parametrization of positive forms...

In the present paper, we introduce a Laguerre type positive linear operators based on the q-integers including the q-Meyer König and Zeller operators defined by Doğru and Duman in [7]. Then we obtain some results about Korovkin type approximation properties and rates of convergence for this generalization. Key-Words: Positive linear operators, q-Meyer König and Zeller operators, qLaguerre polyn...

lorentz characterized the almost convergence through the concept of uniform convergence of de lavallée-poussin mean. in this paper, we generalize the notion of almost convergence by using the concept ofinvariant mean and the generalized de la vallée-poussin mean. we determine the bounded linear operators forthe generalized σ-conservative, σ-regular and σ-coercive matrices.

In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.