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This study is the continuation of our former work [O. Duman and E. Erkus,, Comput. Math. Appl. 52 (2006) 967-974] in which we obtained a statistical Korovkin-type approximation theorem for a sequence of positive linear operators defined on the space of all real-valued continuous and 2 pi periodic functions on the real m-dimensional space. In this paper, we compute the statistical rates of this statistical approximation.

In this paper, we obtain the necessary and sufficient conditions for having the maximum principle and existence of positive solutions for some cooperative systems involving Schrödinger operators defined on unbounded domains. Then, we deduce the existence of solutions for semi-linear systems. Finally we discuss the generalized maximum principle (gf q-positivity) for non cooperative systems.

The aim of this research paper is to establish the following summation formula for the Clausen's series ${; ; }; ; _3F_2$ viz. \[ {; ; }; ; _3F_2\Bigg[ \begin{; ; array}; ; {; ; c}; ; -n, \, \, \, b-a-1, \, \, \, f+1\\ \\b, \, \, \, f \end{; ; array}; ; 1\Bigg] = \frac{; ; (a)_n(c+1)_n}; ; {; ; (b)_n(c)_n}; ; \] where $f= c(1+a-b)/(a-c)$, in {; ; \em three different ways}; ; ; . For $c=\tfrac12 a$, we have \[ {; ; }; ; _3F_2\Bigg[ \begin{; ; array}; ; {; ; c}; ; -n, \, \, \, b-a-1, \, \, \, 2+a-b\\ \\b, \, \, \, 1+a-b \end{; ; array}; ; 1\Bigg] = \frac{; ; (a)_n\big(1+\tfrac12 a\big)_n}; ; {; ; (b)_n\big( \tfrac12 a\big)_n}; ; \] which is already available in the literarute. Our formula is then applied to obtain two general results, one is the Euler's transformation for the series ${; ; }; ; ; 2F_2$ and another is the Kummer-type first transformation for the series ${; ; }; ; _2F_2$ established recently by Paris by following a different method. The results obtained generalize the related results by Exton.

WOS: 000273180800006, In this paper, we introduce new types of sets called (1, 2)*-D(alpha, p) sets, (1, 2)*-D(alpha, s) sets, (1, 2)*-D(c, alpha) sets, (1, 2)*-D(c, s) sets and (1, 2)*-D(c, p) sets new classes of mappings called (1, 2)*-D(alpha, p)continuous, (1, 2)*-D(alpha, s) continuous, (1, 2)*-D(c, alpha) continuous, (1, 2)*-D(c, s) continuous and (1, 2)*-D(c, p) continuous mappings. We obtain several characterizations of these classes, study their bitopological properties, and investigate their relation with other bitopological sets and mappings.

In this paper we establish a class of Hardy-Sobolev type inequalities related to gener- alized Baouendi-Grushin operators. Our results contain the well-known Hardy type inequality and Sobolev type inequality for the class of operators. Furthermore, some new inequalities are obtained.

In this paper we generalize the multivalued contraction theorem of S. B. Nadler (8). As corollaries we obtain fixed point theorems for a multivalued function in complete dislocated metric spaces and complete partial metric space. 1991 Mathematics Subject Classification: 54H25, 47H10

By the use of the corresponding shift matrix, the paper gives a criterion for the unique solvability of linear boundary value problems posed for linear differential algebraic equations up to index 2 with well-matched leading coefficients. The solution is constructed by a proper Green function. Another characterization of the solutions is based upon the description of arbitrary affine linear subspaces of solutions to linear differential algebraic equations in terms of solutions to the adjoint equation. When applied to boundary value problems, the result provides a constructive criterion for unique solvability and allows reducing the problem to initial value problems and linear algebraic equations.

This paper investigates the stabilization of a desired equilibrium point of a model describing the interaction of the immune system (CD4 cells and cyto- toxic T lymphocytes CTL) with human immunodeficiecy virus HIV with sampled- data controllers. The control variable is the drug dose. Two cases of anti-HIV drugs are considered: 1 reverse transcriptase inhibitors (RTI), and 2 protease in- hibitors (PI). The controller is constructed by a variant of the receding horizon con- trol (RHC) method. We use the results obtained by (3) giving su cient conditions which guarantee that the receding horizon controller that stabilizes the approximate discrete-time model also stabilizes the exact discrete-time model for su ciently small discretization parameters. Results of simulations are discussed. Mathematics Subject Classification: 93D15, 93C57, 92D30

The paper is devoted to the study of an approximation process on an unbounded interval representing an integral form in Kantorovich sense of K. Balazs operators. We es- tablish the degree of approximation in some function spaces pointing out the relationship between the local smoothness of functions and the local approximation. By using the mod- ulus of variation, the approximation property in discontinuity points is also examined.