scholarly journals Linear program fixed-point representation

MATEMATIKA ◽  
2017 ◽  
Vol 33 (1) ◽  
pp. 55
Author(s):  
Jalaluddin Morris Abdullah
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Symmetric Matrix ◽  
Fixed Point Problem ◽  
Linear Program ◽  
Point Problem ◽  
Central Elements ◽  
Point Representation ◽  
Primal And Dual Problems ◽  
Primal And Dual

From a linear program and its asymmetric dual, invariant primal and dual problems are constructed. Regular mappings are defined between the solution spaces of the original and invariant problems. The notion of centrality is introduced and subsets of regular mappings are shown to be inversely related surjections of central elements, thus representing the original problems as invariant problems. A fixed-point problem involving an idempotent symmetric matrix is constructed from the invariant problems and the notion of centrality carried over to it; the non-negative central fixed-points are shown to map one-to-one to the central solutions to the invariant problems, thus representing the invariant problems as a fixed-point problem and, by transitivity, the original problems as a fixed-point problem.

Perturbation of the fixed point problem for continuous mappings

2020 ◽  
pp. 241-249
Author(s):  
Zukhra T. Zhukovskaya ◽  
Sergey E. Zhukovskiy
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Continuous Mapping ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Bounded Subset ◽  
Completely Continuous ◽  
Continuous Map ◽  
Continuous Mappings

We consider the problem of a double fixed point of pairs of continuous mappings defined on a convex closed bounded subset of a Banach space. It is shown that if one of the mappings is completely continuous and the other is continuous, then the property of the existence of fixed points is stable under contracting perturbations of the mappings. We obtain estimates for the distance from a given pair of points to double fixed points of perturbed mappings. We consider the problem of a fixed point of a completely continuous mapping on a convex closed bounded subset of a Banach space. It is shown that the property of the existence of a fixed point of a completely continuous map is stable under contracting perturbations. Estimates of the distance from a given point to a fixed point are obtained. As an application of the obtained results, the solvability of a difference equation of a special type is proved.

scholarly journals Several Fixed-Point Theorems for F -Contractions in Complete Branciari b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lili Chen ◽  
Shuai Huang ◽  
Chaobo Li ◽  
Yanfeng Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Related Result ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Well Posedness ◽  
Uniqueness Of Solutions

In this paper, we prove the existence and uniqueness of fixed points for F -contractions in complete Branciari b -metric spaces. Furthermore, an example for supporting the related result is shown. We also present the concept of the weak well-posedness of the fixed-point problem of the mapping T and discuss the weak well-posedness of the fixed-point problem of an F -contraction in complete Branciari b -metric spaces. Besides, we investigate the problem of common fixed points for F -contractions in above spaces. As an application, we apply our main results to solving the existence and uniqueness of solutions for a class of the integral equation and the dynamic programming problem, respectively.

On the theory of fixed point theorems for convex contraction mappings

2015 ◽  
Vol 31 (3) ◽  
pp. 365-371
Author(s):  
VIORICA MURESAN ◽  
◽  
ANTON S. MURESAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Shadowing Property ◽  
Contraction Mappings ◽  
Limit Shadowing

Based on the concepts and problems introduced in [Rus, I. A., The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory, 9 (2008), No. 2, 541–559], in the present paper we consider the theory of some fixed point theorems for convex contraction mappings. We give some results on the following aspects: data dependence of fixed points; sequences of operators and fixed points; well-posedness of a fixed point problem; limit shadowing property and Ulam-Hyers stability for fixed point equations.

scholarly journals The fixed point problem for generalised nonexpansive maps

1997 ◽  
Vol 55 (1) ◽  
pp. 45-61 ◽  
Author(s):  
Michael A. Smyth
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theory ◽  
Normal Structure ◽  
Structure Type ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Nonexpansive Maps

This paper is concerned with extending the theory of the existence of fixed points for generalised nonexpansive maps as far as possible. This can be seen as a continuation of the work of Maurey on the extension of the fixed point theory for nonexpansive maps beyond the requirement of normal structure type conditions.

Coupled fixed points and coupled best proximity points for cyclic Ćirić type operators

2019 ◽  
Vol 26 (1/2) ◽  
pp. 179-196
Author(s):  
Adrian Magdaş
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Coupled Fixed Point ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Best Proximity Points ◽  
Contraction Type ◽  
Coupled Fixed Points

The purpose of this paper is to study the coupled fixed point problem and the coupled best proximity problem for single-valued and multi-valued contraction type operators defined on cyclic representations of the space. The approach is based on fixed point results for appropriate operators generated by the initial problems.

scholarly journals On the geometry of b-distances and the fixed points of mappings

2020 ◽  
Vol 36 (2) ◽  
pp. 241-257
Author(s):  
MITROFAN M. CHOBAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Present Article ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Geometrical Configuration

In the present article we study the geometrical configuration ofb-perturbation of the norm of the normed space.The notion ofb-metric is important in the solving of the fixed point problem.

scholarly journals The theory of some asymptotic fixed point theorems

2014 ◽  
Vol 30 (3) ◽  
pp. 361-368
Author(s):  
ANTON S. MURESAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Fixed Point Problem ◽  
Data Dependence ◽  
Point Problem ◽  
Shadowing Property ◽  
Contraction Mappings ◽  
Limit Shadowing ◽  
Asymptotic Fixed Point

In this paper we present the theory about some fixed point theorems for convex contraction mappings. We give some results on data dependence of fixed points, on sequences of operators and fixed points, on well-possedness of fixed point problem, on limit shadowing property and on Ulam-Hyers stability for equations of fixed points.

scholarly journals The ordered implicit relations and related fixed point problems in the cone $ b $-metric spaces

2022 ◽  
Vol 7 (4) ◽  
pp. 5199-5219
Author(s):  
Anam Arif ◽  
◽  
Muhammad Nazam ◽  
Aftab Hussain ◽  
Mujahid Abbas ◽  
...  
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Existence Of Solution ◽  
Point Problem ◽  
Implicit Relation

<abstract><p>In this paper, we introduce an ordered implicit relation. We present some examples for the illustration of the ordered implicit relation. We investigate conditions for the existence of the fixed points of an implicit contraction. We obtain some fixed point theorems in the cone $ b $-metric spaces and hence answer a fixed-point problem. We present several examples and consequences to explain the obtained theorems. We solve an homotopy problem and show existence of solution to a Urysohn Integral Equation as applications of the obtained fixed point theorem.</p></abstract>

scholarly journals Approximation of common fixed points in 2-Banach spaces with applications

2019 ◽  
Vol 20 (1) ◽  
pp. 43
Author(s):  
D. Ramesh Kumar ◽  
M. Pitchaimani
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Contractive Condition ◽  
Common Fixed Point Problem ◽  
The Common

<p>The purpose of this paper is to establish the existence and uniqueness of common fixed points of a family of self-mappings satisfying generalized rational contractive condition in 2-Banach spaces. An example is included to justify our results. We approximate the common fixed point by Mann and Picard type iteration schemes. Further, an application to well-posedness of the common fixed point problem is given. The presented results generalize many known results on 2-Banach spaces.</p>

scholarly journals Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 158
Author(s):  
Liliana Guran ◽  
Monica-Felicia Bota
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Boundary Value ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Existence Of A Solution ◽  
Shadowing Property ◽  
Limit Shadowing ◽  
Type Boundary ◽  
Cyclic Type

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.

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