scholarly journals Stability of Fixed Point Sets of a Class of Multivalued Nonlinear Contractions

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
Binayak S. Choudhury ◽  
Chaitali Bandyopadhyay
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Hausdorff Distance ◽  
Multivalued Mappings ◽  
Limit Function ◽  
Point Sets ◽  
Nonlinear Contractions ◽  
Fixed Point Sets

We consider a problem of stability of fixed point sets for a sequence of multivalued mappings defined on a metric space converging to a limit function where the convergence is with respect to the Pompeiu-Hausdorff distance. The members of the sequence are assumed to be multivalued almost contractions. We show that the fixed point sets of this sequence of mappings are stable.

Stability results for fixed point sets of α*- Ψ contractive multivalued mappings

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3665-3670
Author(s):  
Binayak Choudhury ◽  
Chaitali Bandyopadhyay ◽  
Rajendra Pant
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Stability Result ◽  
Multivalued Mappings ◽  
Point Sets ◽  
Generalized Contraction ◽  
Class Of Functions ◽  
Stability Results ◽  
Fixed Point Sets

In this paper, we established a stability result for fixed point sets associated with a sequence of multivalued mappings which belong to class of functions obtained by a multivalued extension of certain generalized contraction mapping. Certain other aspects of these mappings are already studied in the existing literatures. We also construct an illustrative example.

scholarly journals Characterization of a b-metric space completeness via the existence of a fixed point of Ciric-Suzuki type quasi-contractive multivalued operators and applications

2019 ◽  
Vol 27 (1) ◽  
pp. 5-33 ◽  
Author(s):  
Hanan Alolaiyan ◽  
Basit Ali ◽  
Mujahid Abbas
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Hausdorff Distance ◽  
Existence And Uniqueness ◽  
Asymptotic Estimate ◽  
Metric Spaces ◽  
Multivalued Operators ◽  
Fixed Point Sets

Abstract The aim of this paper is to introduce Ciric-Suzuki type quasi-contractive multivalued operators and to obtain the existence of fixed points of such mappings in the framework of b-metric spaces. Some examples are presented to support the results proved herein. We establish a characterization of strong b-metric and b-metric spaces completeness. An asymptotic estimate of a Hausdorff distance between the fixed point sets of two Ciric-Suzuki type quasi-contractive multivalued operators is obtained. As an application of our results, existence and uniqueness of multivalued fractals in the framework of b-metric spaces is proved.

Fixed point sets for abstract volterra operators on fréchet spaces

2000 ◽  
Vol 76 (1-2) ◽  
pp. 131-152 ◽  
Author(s):  
Dana M. Bedivan ◽  
Donal O′Regan
Keyword(s):  
Fixed Point ◽  
Fréchet Spaces ◽  
Point Sets ◽  
Volterra Operators ◽  
Fixed Point Sets

The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph

2016 ◽  
Vol 59 (01) ◽  
pp. 3-12 ◽  
Author(s):  
Monther Rashed Alfuraidan
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Orlicz Spaces ◽  
Multivalued Mappings ◽  
Linear Spaces ◽  
Modular Metric Spaces ◽  
Modular Spaces

Abstract We study the existence of fixed points for contraction multivalued mappings in modular metric spaces endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. This paper can be seen as a generalization of Nadler and Edelstein’s fixed point theorems to modular metric spaces endowed with a graph.

scholarly journals Fixed Point Results for the Family of Multivalued F-Contractive Mappings on Closed Ball in Complete Dislocated b-Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 56 ◽  
Author(s):  
Qasim Mahmood ◽  
Abdullah Shoaib ◽  
Tahair Rasham ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Closed Ball ◽  
Multivalued Mappings ◽  
System Of Integral Equations ◽  
Contractive Mappings ◽  
The Family ◽  
Rational Type

The purpose of this paper is to find out fixed point results for the family of multivalued mappings fulfilling a generalized rational type F-contractive conditions on a closed ball in complete dislocated b-metric space. An application to the system of integral equations is presented to show the novelty of our results. Our results extend several comparable results in the existing literature.

scholarly journals Fixed poin sets in digital topology, 1

2020 ◽  
Vol 21 (1) ◽  
pp. 87 ◽  
Author(s):  
Laurence Boxer ◽  
P. Christopher Staecker
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Digital Images ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Point Sets ◽  
Fixed Point Set ◽  
Complete Computation ◽  
Point Set ◽  
Fixed Point Sets

<p>In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results that often differ greatly from standard results in classical topology.</p><p>We introduce several measures related to fixed points for continuous self-maps on digital images, and study their properties. Perhaps the most important of these is the fixed point spectrum F(X) of a digital image: that is, the set of all numbers that can appear as the number of fixed points for some continuous self-map. We give a complete computation of F(C<sub>n</sub>) where C<sub>n</sub> is the digital cycle of n points. For other digital images, we show that, if X has at least 4 points, then F(X) always contains the numbers 0, 1, 2, 3, and the cardinality of X. We give several examples, including C<sub>n</sub>, in which F(X) does not equal {0, 1, . . . , #X}.</p><p>We examine how fixed point sets are affected by rigidity, retraction, deformation retraction, and the formation of wedges and Cartesian products. We also study how fixed point sets in digital images can be arranged; e.g., for some digital images the fixed point set is always connected.</p>

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