Search results for "Fixed-point theorem"
showing 6 items of 96 documents
Fixed point theorems for twisted (α,β)-ψ-contractive type mappings and applications
2013
The purpose of this paper is to discuss the existence and uniqueness of fixed points for new classes of mappings defined on a complete metric space. The obtained results generalize some recent theorems in the literature. Several applications and interesting consequences of our theorems are also given.
Coupled fixed point results in cone metric spaces for -compatible mappings
2011
In this paper, we introduce the concepts of -compatible mappings, b-coupled coincidence point and b-common coupled fixed point for mappings F, G : X × X → X, where (X, d) is a cone metric space. We establish b-coupled coincidence and b-common coupled fixed point theorems in such spaces. The presented theorems generalize and extend several well-known comparable results in the literature, in particular the recent results of Abbas et al. [Appl. Math. Comput. 217, 195-202 (2010)]. Some examples are given to illustrate our obtained results. An application to the study of existence of solutions for a system of non-linear integral equations is also considered. 2010 Mathematics Subject Classificati…
Stoïlow’s theorem revisited
2020
Stoilow's theorem from 1928 states that a continuous, open, and light map between surfaces is a discrete map with a discrete branch set. This result implies that such maps between orientable surfaces are locally modeled by power maps z -> z(k) and admit a holomorphic factorization. The purpose of this expository article is to give a proof of this classical theorem having readers in mind that are interested in continuous, open and discrete maps. (C) 2019 Elsevier GmbH. All rights reserved. Peer reviewed
About Applications of the Fixed Point Theory
2017
AbstractThe fixed point theory is essential to various theoretical and applied fields, such as variational and linear inequalities, the approximation theory, nonlinear analysis, integral and differential equations and inclusions, the dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, and optimisation problems) and mathematical modelling. This paper presents a few benchmarks regarding the applications of the fixed point theory. This paper also debates if the results of the fixed point theory can be applied to the mathematical modelling of quality.
On multivalued weakly Picard operators in partial Hausdorff metric spaces
2015
We discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obtain Kikkawa-Suzuki type fixed point theorems for a new type of generalized contractive conditions. Then, we prove data dependence of a fixed points set theorem. Finally, we present sufficient conditions for well-posedness of a fixed point problem. Our results generalize, complement and extend classical theorems in metric and partial metric spaces.
Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces
2011
The purpose of this paper is to present some fixed point theorems for T -weakly isotone increasing mappings which satisfy a generalized nonlinear contractive condition in complete ordered metric spaces. As application, we establish an existence theorem for a solution of some integral equations.