Zoran Golubović

Fixed Point Theorems of Single-Valued Mapping for c-Distance in Cone Metric Spaces

A new concept of the c-distance in cone metric space has been introduced recently in 2011. The aim of this paper is to extend and generalize some fixed point theorems on c-distance in cone metric space.

Common fixed points of ordered g-quasicontractions and weak contractions in ordered metric spaces

We introduce ordered quasicontractions and g-quasicontractions in partially ordered metric spaces and prove the respective coincidence point and (common) fixed point results. An example shows that the new concepts are distinct from the existing ones. We also prove fixed point theorems for mappings satisfying so-called weak contractive conditions in the setting of partially ordered metric space. Hence, generalizations of several known results are obtained.Mathematics Subject Classification (2010): 47H10; 47N10.

FOURIER'S LAW OF HEAT CONDUCTION IN A NONLINEAR FLUID

The problem of deriving Fouriers law of heat conduction in a nonlinear fluid is considered. As a basis for its derivation, Mullers entropy principle and the assumption introduced by I-Shih Liu are used. It is shown that the absolute temperature, derived in this way, is the same for both linear and nonlinear fluids. Contrary to the absolute temperature, we show that the functional form of the heat flux vector, which characterizes Fouriers law of heat conduction, depends on the first gradient theory of heat conducting fluid.

Modified ψ-contractive mappings in ordered metric spaces and applications

We set up two new variants of ψ-contractive mappings designed for two and three maps in metric spaces and originate common fixed point theorems for T-strictly weakly isotone increasing mappings and relatively weakly increasing mappings in complete ordered metric spaces. To demonstrate our results, we give some examples throughout the paper. At the same time, as applications of the presented theorems, we get hold of common fixed point results for generalized contractions of integral type and we prove an existence theorem for solutions of a system of integral equations.MSC:47H10, 45F05.

Nonlinear cyclic weak contractions in G-metric spaces and applications to boundary value problems

We present fixed point theorems for nonlinear cyclic mappings under a generalized weakly contractive condition in G-metric spaces. We furnish examples to demonstrate the usage of the results and produce an application to second-order periodic boundary value problems for ODEs.MSC:47H10, 34B15.

On the inverse Noether's theorem in nonlinear micropolar continua

In this article, the modified Noethers theorem is established in general form. Then, the inverse theorem is used in nonlinear micropolar continua in order to derive one-parameter family of transformations under which the corresponding functional is invariant. Next, the conservation laws are written. They include, as a special case, the conservation laws of micropolar elastostatics, the balance laws of elastodynamics and elastostatics. We do not analyse any of these special cases, because they may be obtained very easily.

THERMODYNAMICS OF NON-SIMPLE HEAT-CONDUCTING INTERFACE

Abstract Following Moeckels approach, thermodynamics of non-simple, heat-conducting material interface is investigated. In order to obtain field equations for the fields of mass density, motion, and temperature in the interface, specific balance equations are used for mass, momentum, moment of momentum, and energy in the surface, and constitutive equations are stated. The constitutive equations of the bulk material (the three-dimensional non-simple, heat-conducting fluid) were derived by I-Shih Liu. The forms of all of these constitutive equations are restricted by an entropy principle which is adopted from Mullers entropy principle.