In this paper we introduce a broad class of nonlinear mappings which contains the class of contractive mappings and the class of generalized hybrid mappings in a Hilbert space. Then we prove an attractive point theorem for such mappings in a Hilbert space. Furthermore, we prove a mean convergence theorem of Baillon’s type without convexity in a Hilbert space. Finally, we prove a weak convergenc...

In this paper, we first introduce a class of nonlinear mappings called generic generalized nonspreading which contains the class of generalized nonspreading mappings in a Banach space and then prove an attractive point theorem for such mappings in a Banach space. Furthermore, we prove a mean convergence theorem of Baillon’s type and a weak convergence theorem of Mann’s type for such nonlinear m...

Two graphs G1 and G2 of order n pack if there exist injective mappings of their vertex sets into [n], such that the images of the edge sets do not intersect. Sauer and Spencer proved that if (G1) (G2) < 0.5n, then G1 and G2 pack. In this note, we study an Ore-type analogue of the Sauer–Spencer Theorem. Let θ(G) = max{d(u)+ d(v) : uv ∈ E(G)}. We show that if θ(G1) (G2) < n, then G1 and G2 pack. ...

Compiling irregular applications written in a data-parallel language, like Fortran D or High Performance Fortran (HPF), presents a challenge of growing importance. A major component of data-parallel programming is the data mapping, i.e., data distribution and alignment. Map-pings may be either regular, in which case they correspond to simple functions between array indices and owning processors...

metric spaces and approximating fixed points of a pair of contractive type mappings M. Abbas, M. Jovanović, S. Radenović University of Belgrade School of Electrical Engineering http://www.etf.bg.ac.rs JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, Vol. 13, No. 2, pp. 243253, Jan, 2011 References: Abstract: Recently, Chao Wang, Jinghao Zhu, Boško Damjanović, Liang-gen Hu [Approximating fixe...

Based on the technique of enriching contractive type mappings, a that has been used successfully in some recent papers, we introduce concept saturated class mappings. We show that, from this perspective, mappings metric fixed point theory can be separated into two distinct classes, unsaturated and saturated, for any provides genuine new fixed-point results. illustrate by surveying significant r...

The iterates of a uniformly quasiregular map acting on a Riemannian manifold are quasiregular with a uniform bound on the dilatation. There is a Fatou-Julia type theory associated with the dynamical system obtained by iterating these mappings. We construct the first examples of uniformly quasiregular mappings that have a 2-torus as the Julia set. The spaces supporting this type of mappings incl...

is called the modulus of (uniform) continuity of f . The mapping f is said to be uniformly continuous if Ω f (d) → 0 as d ↓ 0. In this case the modulus of continuity is a subadditive monotone continuous function. The definition of Ω f implies that f (Br(x)) ⊂ BΩ f (r)( f (x)). (By Bρ(y) and Bρ(y) we denote, respectively, the open and the closed ball of radius ρ, centered at y.) One important cl...

In this paper, a new mixed type iteration process for approximating common fixed point of two asymptotically nonexpansive self-mappings and nonself-mappings is constructed. We then establish strong convergence theorem under mild conditions in uniformly convex hyperbolic space. The results presented here extend improve some related the literature.