# Mathematica Moravica, Vol. 12-2 (2008)

A Mixed Problem for Navier-Stokes System
Mathematica Moravica, Vol. 12-2 (2008), 1–14.

Abstract. Mixed problems are changed to boundary value problems by making used of Laplace transform. In classical boundary value problems, boundary conditions are local, but boundary conditions could be global ([2, 3, 11]). Every boundary value problem depends on a potential method in mathematical-physics theory. Of course, one couldn't solve some many problems by potential methods. We shall give a method in which one could reduce every boundary value problem to the second kind Fredholm integral equations and then solve it. In fact, we could obtain solution of every local, non-local or global boundary value problem by this method. Finally, we shall give some sufficient conditions for existence of solutions of the Fefferman's problem A ([4]).
Keywords. Navier-Stokes equations, potential theory, boundary conditions.

On de Haan's Uniform Convergence Theorem
Mathematica Moravica, Vol. 12-2 (2008), 15–17.

Abstract. In [Univ. Beograd Publ. Elektrotehn. Fak. Ser. Math. 15 (2004), 85-86], we proved a new inequality for the Lebesgue measure and gave some applications. Here, we present as it new application new short and simple proof of de Haan's uniform convergence theorem.
Keywords. Inequality, Lebesgues measure, uniform convergence.

Common Fixed Point Theorems for Subcompatible D-Maps
Mathematica Moravica, Vol. 12-2 (2008), 19–28.

Abstract. The purpose of this paper is to establish a common fixed point theorem for two pairs of subcompatible single and set-valued $D$-maps in a metric space. This result improves, extends and generalizes the result of [1] and others.
Keywords. Commuting and weakly commuting maps, weakly compatible maps, compatible and compatible maps of type (A), (B) and (C), subcompatible maps, $D$-maps, implicit relations, single and set-valued maps, common fixed point theorems.

Fixed Point Theorems for Some Discontinuous Operators in Cone Metric Space
Mathematica Moravica, Vol. 12-2 (2008), 29–34.

Abstract. In this article, some fixed point theorems in cone metric spaces for operators belonging to the class $E(a,b,c)$ are proved.
Keywords. Fixed point, cone metric space, asymptotically regular.

Sequence with $K_{1}$, $K_{2}$, $K_{n}$, $K_{n+1}$ Mutually Tangent Circles
Mathematica Moravica, Vol. 12-2 (2008), 35–43.

Abstract. In this article is given the formula for radius of circle $K_{n}$, where in sequence $\{K_{j}\}$, four circles $K_{1}$, $K_{2}$, $K_{n}$, $K_{n+1}$, for all $n\geq 3$, are mutually tangent. Radius $r_{n}$ is expressed in terms of radii $r_{1}$, $r_{2}$, $r_{3}$.
Keywords. Sequences of circles, arbelos, Pappus chain.

On Kirk's Fixed Point Main Theorem for Asymptotic Contractions
Mathematica Moravica, Vol. 12-2 (2008), 45–49.

Abstract. We prove that main result of asymptotic contractions by Kirk [J. Math. Anal. Appl. 277 (2003), 645-650, Theorem 2.1, p. 647] has been for the first time proved 17 years ago in Tasković [Fundamental elements of the fixed point theory, ZUNS-1986, Theorem 4, p. 170]. But, the author (and next other authors) this historical fact is to neglect and to ignore.
Keywords. Metric and topological spaces, $TCS$-convergence, complete spaces, contraction, asymptotic contraction, nonlinear conditions for fixed points.

Translational Regular Variation Asymptotic Behavior and Applications
Mathematica Moravica, Vol. 12-2 (2008), 51–76.

Abstract. In this paper we introduce some new classes of functions which are a translational regular asymptotic behavior. In this sense we continue the study of the translational regularly varying functions. This results are closely connected with the Karamata's theory of regularly varying functions.
On the other hand, in this paper we give some theorems of Tauberian nature via the translational regularly varying functions. Applications of new Tauberian theorems and a method of the Monotone Density theorem for Stieltjes transform are considered.
This results are connection with the Karamata's Tauberian theorems, with the Karamata's Hauptsatz, as and with the classical statements of Hardy and Littlewood.
Keywords. Translational slowly varying function, translational regularly varying function, translational $\mathcal{O}$-regularly varying function, uniform convergence, characterization, representation, slowly varying function, regularly varying function, $\mathcal{O}$-regularly varying funct.

Transversal Chaos Spaces and Asymptotic Fixed Points
Mathematica Moravica, Vol. 12-2 (2008), 77–95.