Some Properties of Mappings on Generalized Topological Spaces

This paper considers generalizations of open mappings, closed mappings, pseudo-open mappings, and quotient mappings from topological spaces to generalized topological spaces. Characterizations of these classes of mappings are obtained and some relationships among these classes are established.Comment: 8 papge

Color Visualization of Blaschke Self-Mappings of the Real Projective Plan

The real projective plan $P^2$ can be endowed with a dianalytic structure making it into a non orientable Klein surface. Dianalytic self-mappings of that surface are projections of analytic self-mappings of the Riemann sphere $\widehat{\mathbb{C}}$. It is known that the only analytic bijective self-mappings of $\widehat{\mathbb{C}}$ are the Moebius transformations. The Blaschke products are obtained by multiplying particular Moebius transformations. They are no longer one-to-one mappings. However, some of these products can be projected on $P^2$ and they become dianalytic self-mappings of $P^2$. More exactly, they represent canonical projections of non orientable branched covering Klein surfaces over $P^2$. This article is devoted to color visualization of such mappings. The working tool is the technique of simultaneous continuation we introduced in previous papers.Comment: 16 pages, 5 pages of figure

Existence And Convergence Theorems For Multivalued Generalized Hybrid Mappings In Cat({\kappa})-Space

In this study, we give definition of some multivalued hybrid mappings which are general than many mappings in the existing literature, then we give some existence and convergence results for these mappings in CAT({\kappa})-space

Proper holomorphic mappings into ℓ\ell-concave quadric domains in projective space

In this paper, we prove a type of partial rigidity result for proper holomorphic mappings of certain $\ell$-concave domains in projective space into model quadratic $\ell$-concave domains. The main technical result is a degree estimate for proper holomorphic mappings into the model domains, provided that the mappings extend to projective space as rational mappings, and the source domain contains algebraic varieties and has a boundary with low CR complexity

Growth theorems in slice analysis of several variables

In this paper, we define a class of slice mappings of several Clifford variables, and the corresponding slice regular mappings. Furthermore, we establish the growth theorem for slice regular starlike or convex mappings on the unit ball of several slice Clifford variables, as well as on the bounded slice domain which is slice starlike and slice circular

On Harmonic ν\nu-Bloch and ν\nu-Bloch-type mappings

The aim of this paper is twofold. One is to introduce the class of harmonic $\nu$-Bloch-type mappings as a generalization of harmonic $\nu$-Bloch mappings and thereby we generalize some recent results of harmonic $1$-Bloch-type mappings investigated recently by Efraimidis et al. \cite{EGHV}. The other is to investigate some subordination principles for harmonic Bloch mappings and then establish Bohr's theorem for these mappings and in a general setting, in some cases.Comment: 17 pages; Comments are welcom

The space of initial conditions for linearisable mappings

We apply the algebraic-geometric techniques developed for the study of mappings which have the singularity confinement property to mappings which are integrable through linearisation. The main difference with respect to the previous studies is that the linearisable mappings have generically unconfined singularities. Despite this fact we are able to provide a complete description of the dynamics of these mappings and derive rigorously their growth properties.Comment: 20 pages, 8 figure

Fibers of Polynomial Mappings Over Rn

We prove results on fibers of polynomial mappings Rn ! Rn and deduce when such mappings are surjective under certain conditions

Starlikeness and convexity of polyharmonic mappings

In this paper, we first find an estimate for the range of polyharmonic mappings in the class $HC_{p}^{0}$. Then, we obtain two characterizations in terms of the convolution for polyharmonic mappings to be starlike of order $\alpha$, and convex of order $\beta$, respectively. Finally, we study the radii of starlikeness and convexity for polyharmonic mappings, under certain coefficient conditions

Best proximity point results for almost contraction and application to nonlinear differential equation

Brinde [Approximating fixed points of weak contractions using the Picard itration, Nonlinear Anal. Forum 9 (2004), 43-53] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost $\Theta$- contraction mappings and present some best proximity point results for this new class of mappings. As applications, best proximity point and fixed point results for weak single valued $\Theta$-contraction mappings are obtained. An example is presented to support the results presented herein. An application to a nonlinear differential equation is also provided