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WOS: 000390602900016, We know that every terraced matrix has the factorization R-b = DbC, where C is the Cesaro matrix and D-b = diag {(n + 1)b(n)}. In the present paper, we define the generalized terraced matrix by using the generalized Cesaro matrix in the expression above, and some properties of this matrix are given.

Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a selfmapping on a partial metric space that characterizes the partial metric 0-completeness. In this paper we prove a fixed point result for a new class of contractions of Berinde-Suzuki type on a partial metric space. Moreover, using our results, as application we obtain a new characterization of partial metric 0-completeness. Finally, we give a typical application of fixed point methods to integral equation, by using our results.

WOS: 000359454800010, In this paper, a one-sided condition is given to recover (C, alpha) summability of a sequence from its (A)(C, alpha + 1) summability. Our result extends and generalizes the well known classical Tauberian theorems given for Abel and Cesaro summability methods.

In this paper, we use the order relation on uniform spaces defined by [5] to introduce the notion of compatibility of mappings in an ordered uniform space and use this notion to establish coupled coincidence point theorems to ordered uniform space. An example is also given.

In this paper, we prove a general theorem dealing with generalized absolute convo- lution Ces` aro mean summability factors under weaker conditions by using a general class of increasing sequences instead of an almost increasing sequence. Some new results have also been obtained.

The problem of a multiple player dice tournament is discussed and solved in the paper. A die has a finite number of faces with real numbers written on each. Finite dice sets are proposed which have the following property, defined by Schutte for tournaments: for an arbitrary subset of k dice there is at least one die that beats each of the k with a probability greater than 1/2. It is shown that the proposed dice set realizes the Paley tournament, that is known to have the Schutte property (for a given k) if the number of vertices is large enough. The proof is based on Dirichlet's theorem, stating that the sum of quadratic nonresidues is strictly larger than the sum of quadratic residues.

In this paper, we obtain some new estimations of Iyengar-type inequality in which quasi-convex(quasi-concave) functions are involved. These estimations are improvements of some recently obtained estimations. Some error estimations for the trapezoidal formula are given. Applications for special means are also provided.

In this paper, when approximating a continuos non-negative function on the unit interval, we present an alternative way to the classical Bernstein polynomials. Our new operators become nonlinear, however, for some classes of functions, they provide better error estimations than the Bernstein polynomials. Furthermore, we obtain a simultaneous approximation result for these operators.

In this paper, we establish some new integral inequalities for quasi-convex and h-convex functions by using a kernel and fairly elementary analysis.

The total irregularity of a graph $G$ is defined as $\irr_t(G)=1/2 \sum_{u,v \in V(G)}$ $|d_G(u)-d_G(v)|$, where $d_G(u)$ denotes the degree of a vertex $u \in V(G)$. In this paper we give (sharp) upper bounds on the total irregularity of graphs under several graph operations including join, lexicographic product, Cartesian product, strong product, direct product, corona product, disjunction and symmetric difference., 14 pages, 3 figures, Journal number

In this paper we provide sharp bounds for the Jensen divergence generated by different classes of functions including functions of bounded variation, absolutely continuous, Lipschitz continuous, convex functions and differentiable functions whose derivatives enjoy various prop- erties as mentioned above. The bounds are expressed in terms of known and simpler diver- gence measures that are of importance in various applications such as the analysis of diversity as between and within populations and to cluster analysis. 2010 Mathematics Subject Classification: 26D15; 94017

WOS: 000328081500031, The aims of this paper are introduce the notions of symmetric bi-derivation and generalized derivation in MV-algebras and investigate some of their properties.

In this paper, we present some common fixed point theorems for. ;'/-generalizedf - weakly contractive mappings in metric and ordered metric spaces. Our results extend, generalize and improve some well-known results in the literature. Also, we give an example to illustrate our results. 2000 Mathematics Subject Classification: 54H25; 47H10; 54E50

WOS: 000328081500001, Let R be a prime ring. By a generalized derivation we mean an additive mapping g : R -> R such that g(xy) = g(x)y + xd(y) for all x, y is an element of R where d is a derivation of R. In the present paper our main goal is to generalize some results concerning derivations of prime rings to generalized derivations of prime rings.

In this paper, we use the order relation on partial metric spaces defined by [1] to prove some new fixed point theorems for multivalued monotone mappings in ordered partial metric spaces.

WOS: 000338514500029 In this paper, we study modules with the properties (CRE) and (CREE), which are adapted Zoschinger's modules with the properties (E) and (EE). It is shown that: (1) a module M has the propery (CREE) if and only if every submodule of M has the propery (CRE); (2) a ring R is Rad-supplemented if and only if every left R-module has the propery (CRE); (3) over a commutative Von Neumann regular ring a module M has the propery (CRE) if and only if M is cofinitely injective.

Let fX;Xn;n 1g be a sequence of identically distributed random variables and fai;n;1 i ng be a triangular array of constants. In this short paper, we establish a gene- ral almost sure convergence theorem for the weighted sum SnD P nD1 ai;nXi . Our results improves the works of Sung (14). Furthermore, almost sure convergence theorems of Sn for negatively associated random variables, martingale difference sequence and -mixing sequence are obtained. 2000 Mathematics Subject Classification: 60F15

By the work of Abu Muriefah, Al-Rashed, Dujella and the author, the problem of the existence of D(z)-quadruples in the ring Z[√ -2] has been solved, except for the cases z=24a+2+(12b+6)√ -2, z=24a+5+(12b+6)√ -2, z=48a+44+(24b+12)√ -2. In this paper, we present some new formulas for D(z)-quadruples in these remaining cases, involving some congruence conditions modulo 11 on integers a and b. We show the existence of D(z)-quadruple for significant proportion of the remaining three cases.

WOS: 000338514500017, Let (r, *) be a 2-torsion free *-prime ring with involution * and center Z (R), U a nonzero square closed *-Lie ideal of R. An additive mapping F W R! R is called a generalized derivation if there exits a derivation d WR R such that F. xy/DF. x/yCxd. y/. In the present paper, we prove that U * Z. R/if any one of following conditions holds: 1) O F. u/; u _ D 0; 2) O d. u/; F. v/_ D 0; 3) d. u/oF. v/D 0; 4) O d. u/; F. v/ D * O u; v; 5) d. u/oF (v) D * uov; 6) d. u/F. v/* uv 2 Z. R/; for all u; v 2 U: Furthermore, an example is given to demonstrate that the *-primeness hypothesis is not superfluous.

In this paper, we introduce a generalization of the Stancu- Schurer operators based on q-integers and get a Bohman-Korovkin type approximation theorem of these operators. We also compute the rate of convergence by using the first modulus of smoothness and give some numerical result of operators based on Matlab algorithms. 2000 Mathematics Subject Classification: 41A36

In this paper we present some existence, uniqueness and Hyers-Ulam stability results for the coupled fixed point of a pair of contractive type operators on complete metric spaces. The approach is based on a Perov type fixed point theorem for contractions. Some applications to integral equations and to boundary value problems are also given. 2000 Mathematics Subject Classification: 47H10; 54H25

In this paper, we establish some new integral inequalities for convex and m-convex functions by using a new kernel. The analysis used in the proofs is fairly elementary and based on the classical inequalities. We also give some comparisons and applications to special means for our results.

Sufficient conditions guaranteeing the existence of three positive solutions of the multi-point boundary value problem for the infinite difference equation {Delta[p(n)phi(Delta x(n))] + f(n, x(n). Delta x(n)) = 0, n is an element of N-0, x(0) - Sigma(infinity)(n=1) alpha(n)x(n) = 0, lim(n ->+infinity) x(n)/1+Sigma(n-1)(s=0) 1/phi(-1)(p(s)) - Sigma(infinity)(n=1) beta(n)x(n) = 0, are established using a fixed point theorem. It is the purpose of this paper to show that this approach of obtaining positive solutions of BVPs by using multi-fixed-point theorems can be extended to infinite difference equations containing the nonlinear operator Delta[p phi(Delta x)]. The possible solutions of this BVP are not concave if p(n) not equivalent to constant.

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.