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Content available remote Some relations including various linear operators
Making use of the Carlson-Schaer linear operator, some subclasses of analytic functions are studied. Some relations including various linear operators are given.
Content available remote A linear operator and associated class of multivalent analytic functions
We introduce a certain class H alpha/k (p, lambda;h) of multivalent analytic functions in the open unit disc involving a linear operator L alpha/k. The aim of this paper is to extend the similar concept of many earlier papers. We use techniques of differential subordination and convolution of this class.
Content available remote Order properties of the space of A-linear operators
Let A be an f-algebra with unit and L, M be two topologically full f-modules on A. We prove that the space of A-linear operators Lb(L, M; A) is a Riesz space and we study the order properties of the adjoint operator from Lb(L, M; A) to Lb(M~, L~; (A)^n). The main result given here describes the centre of the space of Lb{L, M; A).
Content available remote The Kantorovich form of Schurer-Stancu operators
Content available remote Optimal supervisory control of regular languages
This paper presents an algorithm for optimal control of regular languages, realized as deterministic finite state automata (DFSA), with (possible) penalty on event disabling. A signed real measure quantifies the behavior of controlled sublanguages based on a state transition cost matrix and a characteristic vector as reported in an earlier publication. The performance index for the proposed optimal policy is obtained by combining the measure of the supervised plant language with the cost of disabled controllable event(s). Synthesis of this optimal control policy requires at most n iterations, where n is the number of states of the DFSA model generated from the unsupervised regular language. The computational complexity of the optimal control synthesis is polynomial in n. The control algorithms are illustrated with an application example of a twin-engine surveillance aircraft.
Content available remote On some right invertible operators in differential spaces
In this paper we consider the right invertibility problem of some linear operators defined on the algebra of smooth function on a differential space.
By introducing a new class of analytic functions with negative coefficients which involves the Wright's generalized hypergeometric function, we investigate the coefficient bounds, distortion theorems, extreme points and radii of convexity and starlikeness for this class of functions.
Content available remote Statistical approximation for periodic functions
In this paper we study a Korovkin type approximation theorem for positive linear operators on the space of all 2(pi)-periodic and continuous functions on the whole real axis via A-statistical convergence.
According to Mickael's selection theorem any surjective continuous linear operator from one Prechet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if E is a Frechet space and T : E -> E is a continuous linear operator such that the Cauchy problem x = T x, x(0) = X0 is solvable in [0,1] for any X06 E, then for anyf zawiera się C([0, 1],E), there exists a continues map S : [0,1] x E -> E, (t x) ->o StX such that for any X0 zawiera się w E, the function x(t) = StX0 is a solution of the Cauchy problem x(t) = Tx(t) +- f(t), x(0) = X0 (they call S a fundamental system of solutions of the equation x = Tx + f). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Frechet spaces and strong duals of Frechet-Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.
The object of the present paper is to introduce two subclasses Bk,p (a, c) and Ck,p (a, c) of analytic functions in the open unit disc involving a linear operator [...] (a, c) and derive some properties of these classes.
The supremum norm of the generalized shift operator S phi on the space BMO(R) is estimated, provided phi is an increasing and absolutely continuous homeomorphic self-mapping of R and phi' is an elemnt of BMO(R) andlog phi'II. is small. This result is extended to a locally rectifiable Jordan arc in C which is homeomorphic to R.
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