Dimension of faces generated by certain positive linear operators

Dimension of Certain Kernel Spaces of Linear Operators

Let G be a semigroup of linear operators on a vector space S into itself with the operation of composition. A subset of G may be associated with a matroid X . We discuss the dimension of the kernels of certain linear operators induced in a natural way by the matroid structure on X .

Approximation of functions of two variables by certain linear positive operators

Abstract. We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using modulus of continuity. Moreover we define an rth order generalization of these operators and observe its approximation properties. Furthermore, we study ...

Uniform weighted approximation by positive linear operators

We characterize the functions defined on a weighted space, which are uniformly approximated by a sequence of positive linear operators and we obtain the range of the weights which can be used for uniform approximation. We, also, obtain an estimation of the remainder in terms of the usual modulus of continuity. We give particular results for the Szász-Mirakjan and Baskakov operators. Mathematics...

Univalence of Certain Linear Operators Defined by Hypergeometric Function

On Ascertaining Inductively the Dimension of the Joint Kernel of Certain Commuting Linear Operators

Given an index set X, a collection IB of subsets of X (all of the same cardinality), and a collection f`xgx2X of commuting linear maps on some linear space, the family of linear operators whose joint kernel K = K(IB) is sought consists of all `A :=Qa2A `a with A any subset of X which intersects every B 2 IB. The goal is to establish conditions, on IB and `, which ensure that dimK(IB) = X B2IBdi...