The notion of an asymptotic center is used to prove a number of results concerning the existence of fixed points under certain selfmappings of a closed and bounded convex subset of a uniformly convex Banach space.

A zone diagram is a relatively new concept which has emerged in computational geometry and is related to Voronoi diagrams. Formally, it is a fixed point of a certain mapping, and neither its uniqueness nor its existence are obvious in advance. It has been studied by several authors, starting with T. Asano, J. Matoušek and T. Tokuyama, who considered the Euclidean plane with singleton sites, and...

In this paper, most of classical and modern convergence theorems of iterative schemes for nonexpansive mappings are presented and the main results in the paper generalize and improve the corresponding results given by many authors. 2000 Mathematics Subject Classification: Primary 47H17; secondary 47H05, 47H10.

We develop the convergence analysis of discontinuous Galerkin finite element approximations to second-order quasilinear elliptic and hyperbolic systems of partial differential equations of the form, respectively, − ∑d α=1 ∂xαSiα(∇u(x)) = fi(x), i = 1, . . . , d, and ∂2 t ui− ∑d α=1 ∂xαSiα(∇u(t, x)) = fi(t, x), i = 1, . . . , d, with ∂xα = ∂/∂xα, in a bounded spatial domain in R d, subject to mi...

The failure of uniform dependence on the data is an interesting property classical solution for a hyperbolic system. In this paper, we consider map Cauchy problem to 2D viscous shallow water equations, which hyperbolic–parabolic We give new approach studying issue nonuniform initial these equations. prove that not uniformly continuous in Sobolev spaces H s × $H^s\times H^{s}$ > 2 $s>2$ .

We study the construction and the convergence of the Ishikawa iterative process with errors for nonexpansive mappings in uniformly convex Banach spaces. Some recent corresponding results are generalized. 2000 Mathematics Subject Classification. 47H10, 40A05.

In this survey we present some recent applications of proof mining to the fixed point theory of (asymptotically) nonexpansive mappings and to the metastability (in the sense of Terence Tao) of ergodic averages in uniformly convex Banach spaces.

In this paper, we first introduce the class of generalized nonexpansive mappings in Banach spaces. This class contains both the classes of nonexpansive and ̨-nonexpansive mappings. In addition, we obtain some fixed point and coincidence point theorems for generalized nonexpansive mappings in uniformly convex Banach spaces. Our results extend some wellknown results in literature. 2010 Mathematic...

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...