Special Issue "Fixed Point Theorems and Applications"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (30 June 2016).

Special Issue Editor

Prof. Dr. Pasquale Vetro

Guest Editor
Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy
Interests: fixed point theory; general topology; operator theory; real functions

Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to promote research and discussion on fixed points of mappings and operators. It will reflect on the status of theoretical research on fixed point theory and their advanced applications to the solution of practical problems. A particular attention will be given to results concerning the solvability of integro-differential equations and inclusions, of which advanced applications include fluid mechanics, viscoelasticity and many other physical phenomena.

Potential topics include, but are not limited to:

  • Fixed point theorems in abstract spaces.
  • Properties of the fixed point set: data dependence, stability, well posedness.
  • Integro-differential equations and applications.
  • Operator equations and inclusions in abstract spaces.

Prof. Dr. Pasquale Vetro
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Differential equations
  • Fixed points
  • Integral operators
  • Metric spaces
  • Operator inclusions

Published Papers (4 papers)

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Research

Open AccessArticle
Fixed Points of Set Valued Mappings in Terms of Start Point on a Metric Space Endowed with a Directed Graph
Mathematics 2017, 5(2), 24; https://doi.org/10.3390/math5020024 - 19 Apr 2017
Cited by 1
Abstract
In the present article, we introduce the new concept of start point in a directed graph and provide the characterizations required for a directed graph to have a start point. We also define the notion of a self path set valued map and [...] Read more.
In the present article, we introduce the new concept of start point in a directed graph and provide the characterizations required for a directed graph to have a start point. We also define the notion of a self path set valued map and establish its relation with start point in the setting of a metric space endowed with a directed graph. Further, some fixed point theorems for set valued maps have been proven in this context. A version of the Knaster–Tarski theorem has also been established using our results. Full article
(This article belongs to the Special Issue Fixed Point Theorems and Applications)
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Open AccessArticle
On Optimal Fuzzy Best Proximity Coincidence Points of Proximal Contractions Involving Cyclic Mappings in Non-Archimedean Fuzzy Metric Spaces
Mathematics 2017, 5(2), 22; https://doi.org/10.3390/math5020022 - 01 Apr 2017
Cited by 6
Abstract
The main objective of this paper is to deal with some properties of interest in two types of fuzzy ordered proximal contractions of cyclic self-mappings T integrated in a pair (g,T) of mappings. In particular, g is a non-contractive [...] Read more.
The main objective of this paper is to deal with some properties of interest in two types of fuzzy ordered proximal contractions of cyclic self-mappings T integrated in a pair ( g , T ) of mappings. In particular, g is a non-contractive fuzzy self-mapping, in the framework of non-Archimedean ordered fuzzy complete metric spaces and T is a p -cyclic proximal contraction. Two types of such contractions (so called of type I and of type II) are dealt with. In particular, the existence, uniqueness and limit properties for sequences to optimal fuzzy best proximity coincidence points are investigated for such pairs of mappings. Full article
(This article belongs to the Special Issue Fixed Point Theorems and Applications)
Open AccessArticle
A Generalization of b-Metric Space and Some Fixed Point Theorems
Mathematics 2017, 5(2), 19; https://doi.org/10.3390/math5020019 - 23 Mar 2017
Cited by 36
Abstract
In this paper, inspired by the concept of b-metric space, we introduce the concept of extended b-metric space. We also establish some fixed point theorems for self-mappings defined on such spaces. Our results extend/generalize many pre-existing results in literature. Full article
(This article belongs to the Special Issue Fixed Point Theorems and Applications)
Open AccessArticle
A New Approach to Study Fixed Point of Multivalued Mappings in Modular Metric Spaces and Applications
Mathematics 2016, 4(3), 51; https://doi.org/10.3390/math4030051 - 08 Aug 2016
Cited by 3
Abstract
The purpose of this paper is to present a new approach to study the existence of fixed points for multivalued F-contraction in the setting of modular metric spaces. In establishing this connection, we introduce the notion of multivalued F-contraction and prove [...] Read more.
The purpose of this paper is to present a new approach to study the existence of fixed points for multivalued F-contraction in the setting of modular metric spaces. In establishing this connection, we introduce the notion of multivalued F-contraction and prove corresponding fixed point theorems in complete modular metric space with some specific assumption on the modular. Then we apply our results to establish the existence of solutions for a certain type of non-linear integral equations. Full article
(This article belongs to the Special Issue Fixed Point Theorems and Applications)
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