Fixed Point Theory in Ordered Sets from the Metric Point of View

2013 ◽  
pp. 223-236
Author(s):  
M. Z. Abu-Sbeih ◽  
M. A. Khamsi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Point Of View ◽  
Ordered Sets

scholarly journals On Fuzzy Orders and Metrics

2014 ◽  
Vol 10 ◽  
pp. 48-52
Author(s):  
Vinayak E. Nikumbh
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Ordered Sets

In this paper we present results regarding fixed point theory using notion of fuzzy orders.We propose anapproach based on quasi metrics which in a way unifies the fixed point theory for ordered sets and metric spaces.

scholarly journals Convergence theorems for fixed point iterative methods defined as admissible perturbations of a nonlinear operator

2013 ◽  
Vol 29 (1) ◽  
pp. 9-18
Author(s):  
VASILE BERINDE ◽  
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Nonlinear Operator ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Point Of View ◽  
Iterative Approximation ◽  
Convergence Theorems ◽  
Fixed Point Iterative Method

The aim of this paper is to prove some convergence theorems for a general fixed point iterative method defined by means of the new concept of admissible perturbation of a nonlinear operator, introduced in [Rus, I. A., An abstract point of view on iterative approximation of fixed points, Fixed Point Theory 13 (2012), No. 1, 179–192]. The obtained convergence theorems extend and unify some fundamental results in the iterative approximation of fixed points due to Petryshyn [Petryshyn, W. V., Construction of fixed points of demicompact mappings in Hilbert space, J. Math. Anal. Appl. 14 (1966), 276–284] and Browder and Petryshyn [Browder, F. E. and Petryshyn, W. V., Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), No. 2, 197–228].

scholarly journals On Best Proximity Points under the -Property on Partially Ordered Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mohamed Jleli ◽  
Erdal Karapinar ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Best Proximity Point ◽  
Point Theory ◽  
Point Of View ◽  
Ordered Metric Spaces

Very recently, Abkar and Gabeleh (2013) observed that some best proximity point results under the -property can be obtained from the same results in fixed-point theory. In this paper, motivated by this mentioned work, we show that the most best proximity point results on a metric space endowed with a partial order (under the -property) can be deduced from existing fixed-point theorems in the literature. We present various model examples to illustrate this point of view.

A general principle on ordered sets and its applications to fixed point theory

1989 ◽  
Vol 34 (1-2) ◽  
pp. 129-137 ◽  
Author(s):  
Sun Jingxian ◽  
Sun Yong
Keyword(s):  
Fixed Point ◽  
General Principle ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Ordered Sets

SOL: an exercise in defining a language

1979 ◽  
Vol 2 (1) ◽  
pp. 337-349
Author(s):  
A. Maggiolo-Schettini ◽  
G. Uccella
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Point Of View ◽  
Input Output ◽  
Semantic Point ◽  
Recursive Systems

A language for operation on a stack (SOL) is defined formally, also from the semantic point of view. The semantics is an input-output semantics which uses functions from sequences (of integers) of indefinite length to sequences (of integers) of indefinite length as models of the computation on a stack. The programs in SOL are interpreted in recursive systems of functional definitions to which fixed point theory easily applies in order to evaluate the functions computed by the programs. The language has been implemented and used for didactic purposes.

scholarly journals Applications of Fixed Point Theory to Investigate a System of Fractional Order Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Zareen A. Khan ◽  
Israr Ahmad ◽  
Kamal Shah
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Point Of View ◽  
Existence Theory ◽  
Solution Stability ◽  
Main Work ◽  
Fractional Differential ◽  
Hadamard Derivative

We investigate a nonlinear system of pantograph-type fractional differential equations (FDEs) via Caputo-Hadamard derivative (CHD). We establish the conditions for existence theory and Ulam-Hyers-type stability for the underlying boundary value system (BVS) of FDE. We use Krasnoselskii’s and Banach’s fixed point theorems to obtain the desired results for the existence of solution. Stability is an important aspect from a numerical point of view we investigate here. To justify the main work, relevant examples are provided.

Convergence results for fixed point iterative algorithms in metric spaces

2019 ◽  
Vol 35 (2) ◽  
pp. 209-220
Author(s):  
IOAN A. RUS ◽  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Iterative Algorithms ◽  
Point Theory ◽  
Point Of View ◽  
Iterative Approximation ◽  
Research Directions ◽  
Convergence Results ◽  
Convergence Of Algorithm

In this paper we give some conditions on fn and f which imply the convergence of algorithm (2). In this way we improve some results given in [Rus, I. A., An abstract point of view on iterative approximation of fixed points: impact on the theory of fixed point equations, Fixed Point Theory, 13 (2012), No. 1, 179–192]. In our results, in general we do not suppose that, Ff 6= ∅. Some research directions are formulated.

Sign in / Sign up

Export Citation Format

Share Document