Sharp bounds for the Neuman-Sándor mean and for the logarithmic mean are established. The bounding quantities are the one-parameter bivariate means called the p-means. In this paper best values of the parameters of the bounding means are obtained. Mathematics subject classification (2010): 26E60, 26D07, 26D20.

In this paper, we deal with the problem of meromorphic functions that have three weighted sharing values, and obtain a uniqueness theorem which improves those given by Ozawa, H. X. Yi, I. Lahiri, Q. C. Zhang, and others. Some examples are provided to show that the results in this paper are the best possible. 2000 Mathematics Subject Classification: 30D30, 30D35

We present the best possible parameters p,q ∈ (0,1] such that the double inequality 1 3p2 cos(px)+ 1− 1 3p2 < sin(x) x < 1 3q2 cos(qx)+ 1− 1 3q2 holds for all x ∈ (0,π/2) . As applications, some new inequalities for the sine integral, Catalan constant and Schwab-Borchardt mean are found. Mathematics subject classification (2010): 26D05, 26E60.

We prove that, for every simple polygon P having k ≥ 1 reflex vertices, there exists a point q ∈ P such that every half-polygon that contains q contains nearly 1/2(k + 1) times the area of P . We also give a family of examples showing that this result is the best possible. Mathematics Subject Classification (2010). 51E99.

By using the methods of weight functions and Hermite-Hadamard’s inequality, two kinds of more accurate equivalent reverse multidimensional half-discrete Hilbert-type inequalities with the kernel of hyperbolic cotangent function are given. The constant factor related to the Riemann zeta function is proved to be the best possible. Mathematics subject classification (2010): 26D15, 47A07, 37A10.

We give a slight improvement of the best known lower bound for the supremum of autoconvolutions of nonnegative functions supported in a compact interval with a fixed integral. Also, by means of explicit examples we disprove a long standing natural conjecture of Schinzel and Schmidt concerning the extremal function for such autoconvolutions. 2000 Mathematics Subject Classification. Primary 42A85...

Due to the Lagrange interpolation polynomials do not converge uniformly to arbitrary continuous functions, in this paper, a new interpolation polynomial is constructed by using the weighted average method to the interpolated functions. It is proved that the interpolation polynomial not only converges uniformly to arbitrary continuous functions, but also has the best approximation order and the ...

The paper investigates the notion of Pareto-Nash equilibrium as continuation of the works [2–4]. Problems and basic theoretical results are exposed. Method of intersection of graphs of best response mappings [3] is applied to solve the dyadic two-criteria games. Mathematics Subject Classification 2000: 91A05, 91A06, 91A10, 91A43, 91A44.

Graph bisection is an elementary problem in graph theory. We consider the best known experimental algorithms and introduce a new algorithm called Longest-Path-Algorithm. Applying this algorithm to the cluster tree generation of hierarchical matrices, arising for example in discretizations of partial equations, we show that this algorithm outperforms previous algorithms. Mathematics Subject Clas...

The Nash equilibria set (NES) is described as an intersection of graphs of best response mappings. The problem of NES computing for multi-matrix extended games is considered. A method for NES computing is studied. Mathematics Subject Classification 2000: 91A05, 91A06, 91A10, 91A44, 90C05, 90C31, 90C90.