2,075 research outputs found
Partial metric spaces with negative distances and fixed point theorems
In this paper we consider partial metric spaces in the sense of O'Neill. We
introduce the notions of strong partial metric spaces and Cauchy functions. We
prove a fixed point theorem for such spaces and functions that improves
Matthews' contraction mapping theorem in two ways. First, the existence of
fixed points now holds for a wider class of functions and spaces. Second, our
theorem also allows for fixed points with nonzero self-distances. We also prove
fixed point theorems for orbitally -contractive and orbitally
-contractive maps. We then apply our results to give alternative proofs
of some of the other known fixed point theorems in the context of partial
metric spaces.Comment: 19 page
Numerics and Fractals
Local iterated function systems are an important generalisation of the
standard (global) iterated function systems (IFSs). For a particular class of
mappings, their fixed points are the graphs of local fractal functions and
these functions themselves are known to be the fixed points of an associated
Read-Bajactarevi\'c operator. This paper establishes existence and properties
of local fractal functions and discusses how they are computed. In particular,
it is shown that piecewise polynomials are a special case of local fractal
functions. Finally, we develop a method to compute the components of a local
IFS from data or (partial differential) equations.Comment: version 2: minor updates and section 6.1 rewritten, arXiv admin note:
substantial text overlap with arXiv:1309.0243. text overlap with
arXiv:1309.024
Fixed point theorems for --contractive mappings of Meir--Keeler type and applications
In this paper, we introduce the notion of --contractive mapping of
Meir--Keeler type in complete metric spaces and prove new theorems which assure
the existence, uniqueness and iterative approximation of the fixed point for
this type of contraction. The presented theorems extend, generalize and improve
several existing results in literature. To validate our results, we establish
the existence and uniqueness of solution to a class of third order two point
boundary value problems
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