Received: December 21, 2010 Accepted: January 7, 2011 doi:10.5539/jmr.v3n2p151 Abstract In this paper, we study fixed point theorems for multi-valued weak contractions. We show that the Picard projection iteration converges to a fixed point, give a rate of convergence and generalize Collage theorem. This work includes results on multi-valued contraction mappings studied by (Kunze, H.E., La Torr...

In this paper we study a nonlinear system of differential equations which arises from a stationary 2-dimensional Ice-Sheet Model describing the ice-streaming phenomenon. The system consists of a multivalued nonlinear PDE of parabolic type coupled with a first order PDE and an ODE involving a nonlocal term. We study the uniqueness of weak solution under suitable assumptions (physically reasonabl...

We establish a fixed point theorem for a continuous function f : X → E, where E is a Banach space and X ⊆ E. Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented.

Bipotentials are non smooth mechanics tools, used to model various non associative multivalued constitutive laws of dissipative materials (friction contact, soils, cyclic plasticity of metals, damage). Given by a graph M representing a multivalued constitutive law, we state a simple necessary and sufficient condition for the existence of a bipotential b for which M is the set of (x, y) such tha...

Since the fundamental theory of variational inequality was founded in the 1960s, the variational inequality theory with applications has made powerful progress and has become an important part of nonlinear analysis. It has been applied intensively to mechanics, differential equation, cybernetics, quantitative economics, optimization theory, nonlinear programming, and so forth (see [2]). In virt...

Let (X,H) be a pair of a smooth rational surface X and an ample divisor H on X . Assume that (KX , H) < 0. Let MH(r, c1, χ) be the moduli space of semi-stable sheaves E of rk(E) = r, c1(E) = c1 and χ(E) = χ. To consider relations between moduli spaces of different invariants is an interesting problem. If (c1, H) = 0 and χ ≤ 0, then Maruyama [Ma2], [Ma3] studied such relations and constructed a ...

Darbo fixed point theorem is a powerful tool which used in many fields mathematics. Because of this feature, generalizations and its relations with other subjects have been investigated. Here we introduce generalization an F - contraction type mapping define new by using both function lasses uniformly convergent sequences functions examine some properties. Afterward, show that the contraction, ...

Using two models that incorporate a nonlinear forward-backward heat equation, we demonstrate the existence of well-deened weak solutions containing shocks for diiusive problems. Occurrence of shocks is connected to multivalued inverse solutions and non-monotone potential functions. Unique viscous solutions are determined from perturbation theory by matching to a shock layer condition. Results o...