Let f : D → D ′ be a proper holomorphic mapping between bounded domains D, D ′ in C 2. Let M, M ′ be open pieces on ∂D, ∂D ′ respectively that are smooth, real analytic and of finite type. Suppose that the cluster set of M under f is contained in M ′. It is shown that f extends holomorphically across M. This can be viewed as a local version of the Diederich-Pinchuk extension result for proper m...

We prove a geometric logarithmic derivative lemma for rigid analytic mappings to algebraic varieties in characteristic zero. We use the lemma to give a new and simpler proof (at least in characteristic zero) of Berkovich’s little Picard theorem [Ber, Theorem 4.5.1], which says there are no nonconstant rigid analytic maps from the affine line to non-singular projective curves of positive genus, ...

We prove a geometric logarithmic derivative lemma for rigid analytic mappings to algebraic varieties in characteristic zero. We use the lemma to give a new and simpler proof (at least in characteristic zero) of Berkovich’s little Picard theorem, which says there are no nonconstant rigid analytic maps from the affine line to nonsingular projective curves of positive genus, and of Cherry’s result...

In this paper, we give some results on the common fixed point of self-mappings defined on complete $b$-metric spaces. Our results generalize Kannan and Chatterjea fixed point theorems on complete $b$-metric spaces. In particular, we show that two self-mappings satisfying a contraction type inequality have a unique common fixed point. We also give some examples to illustrate the given results.

‎inspired by the work of suzuki in‎ ‎[t. suzuki‎, ‎a generalized banach contraction principle that characterizes metric completeness‎, proc‎. ‎amer‎. ‎math‎. ‎soc. ‎136 (2008)‎, ‎1861--1869]‎, ‎we prove a fixed point theorem for contractive mappings‎ ‎that generalizes a theorem of geraghty in [m.a‎. ‎geraghty‎, ‎on contractive mappings‎, ‎proc‎. ‎amer‎. ‎math‎. ‎soc., ‎40 (1973)‎, ‎604--608]‎an...

The aim of this paper is to extend the Kannan fixed point theorem from single-valued self mappings T : X → X to mappings F : X3 → X satisfying a Prešić-Kannan type contractive condition: d (F (x, y, z) , F (y, z, u)) ≤ k 8 [d (x, F (x, y, z)) + d (y, F (y, x, y))+ +d (z, F (z, y, x)) + d (y, F (y, z, u)) + d (z, F (z, y, z)) + d (u, F (u, z, y))], or a Prešić-Chatterjea type contractive conditi...

The aim of this note is to give a type of characterization of Banach spaces in terms of the stability of functional equations. More precisely, we prove that a normed space X is complete if there exists a functional equation of the type n ∑ i=1 aif(φi(x1, . . . , xk)) = 0 (x1, . . . , xk ∈ D) with given real numbers a1, . . . , an, given mappings φ1 . . . , φn : D k → D and unknown function f : ...

a common fixed point result for weakly increasing mappings satisfying generalized contractive type of zhang in ordered metric spaces are derived.

in this paper, we introduce a new concept of - -ϕ-contractive integral type mappings and establish some new xed point theorems in complete metric spaces.

A complete characterization of proper holomorphic mappings between domains from the class of all pseudoconvex Reinhardt domains in C with the logarithmic image equal to a strip or a half-plane is given. 1. Statement of results We adopt here the standard notations from complex analysis. Given γ = (γ1, γ2) ∈ R 2 and z = (z1, z2) ∈ C 2 for which it makes sense we put |z | = |z1| γ1 |z2| γ2 . The u...