Topic Editors

Dr. Safeer Hussain Khan
Department of Mathematics and Statistics, North Carolina A&T State University, Greensboro, NC 27411, USA
School of Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, UK
Department of Mathematics, Morgan State University, Baltimore, MD 21251, USA

Fixed Point Theory and Measure Theory

Abstract submission deadline
30 September 2025
Manuscript submission deadline
30 November 2025
Viewed by
3784

Topic Information

Dear Colleagues,

The interdisciplinary topic of “Fixed Point Theory and Measure Theory” presents a rich area for research, blending the study of invariant points under mappings with the properties and structures of measurable spaces. The scope of the intersection of these theories is the advanced exploration of research topics such as the following: functional analysis, fixed points of measure-preserving transformations, ergodic theory, dynamical systems, stochastic fixed point problems (such as in Markov processes), random fixed point theory, optimization problems involving measures, game theory, equilibrium problems, fixed points of integrable or measurable functions, the interplay between the topological properties of measure spaces and fixed point results, and so on. The aim of integrating fixed point theory with measure theory is to develop a deeper understanding of how measure theoretic properties influence the behavior of fixed points and vice versa. Contributions can include, but are not limited to, the following: formulating and proving new fixed point theorems that are influenced by measure theoretic constraints and exploring how these results generalize or refine existing theorems; creating novel methodologies and techniques that leverage the synergy between these two fields to solve complex problems, including those involving non-standard spaces or measures; and encouraging collaboration between mathematicians specializing in fixed point theory, measure theory, and their applications to promote innovative solutions and new lines of research. We also welcome independent results from both fields as they may instigate the beginning of new research collaborations and cultivate new areas of research when considered together.

Dr. Safeer Hussain Khan
Dr. Lateef Olakunle Jolaoso
Dr. Olaniyi S. Iyiola
Topic Editors

Keywords

  • fixed points
  • measure
  • measurable functions
  • topological properties of measure spaces
  • ergodic theory
  • dynamical systems
  • stochastic fixed points as in Markov processes
  • random fixed point
  • optimization
  • game theory
  • equilibrium problems

Participating Journals

Journal Name Impact Factor CiteScore Launched Year First Decision (median) APC
AppliedMath
appliedmath
0.7 1.1 2021 23.5 Days CHF 1200 Submit
Axioms
axioms
1.6 - 2012 21.6 Days CHF 2400 Submit
Fractal and Fractional
fractalfract
3.3 6.0 2017 19.9 Days CHF 2700 Submit
Mathematics
mathematics
2.2 4.6 2013 18.4 Days CHF 2600 Submit
Symmetry
symmetry
2.2 5.3 2009 17.1 Days CHF 2400 Submit

Preprints.org is a multidisciplinary platform offering a preprint service designed to facilitate the early sharing of your research. It supports and empowers your research journey from the very beginning.

MDPI Topics is collaborating with Preprints.org and has established a direct connection between MDPI journals and the platform. Authors are encouraged to take advantage of this opportunity by posting their preprints at Preprints.org prior to publication:

  1. Share your research immediately: disseminate your ideas prior to publication and establish priority for your work.
  2. Safeguard your intellectual contribution: Protect your ideas with a time-stamped preprint that serves as proof of your research timeline.
  3. Boost visibility and impact: Increase the reach and influence of your research by making it accessible to a global audience.
  4. Gain early feedback: Receive valuable input and insights from peers before submitting to a journal.
  5. Ensure broad indexing: Web of Science (Preprint Citation Index), Google Scholar, Crossref, SHARE, PrePubMed, Scilit and Europe PMC.

Published Papers (3 papers)

Order results
Result details
Journals
Select all
Export citation of selected articles as:
17 pages, 344 KB  
Article
On Some Classes of Enriched Cyclic Contractive Self-Mappings and Their Boundedness and Convergence Properties
by Manuel De la Sen
Mathematics 2025, 13(18), 2948; https://doi.org/10.3390/math13182948 - 11 Sep 2025
Viewed by 122
Abstract
This paper focuses on dealing with several types of enriched cyclic contractions defined in the union of a set of non-empty closed subsets of normed or metric spaces. In general, any finite number p2 of subsets is permitted in the cyclic [...] Read more.
This paper focuses on dealing with several types of enriched cyclic contractions defined in the union of a set of non-empty closed subsets of normed or metric spaces. In general, any finite number p2 of subsets is permitted in the cyclic arrangement. The types of examined single-valued enriched cyclic contractions are, in general, less stringent from the point of view of constraints on the self-mappings compared to p-cyclic contractions while the essential properties of these last ones are kept. The convergence of distances is investigated as well as that of sequences generated by the considered enriched cyclic mappings. It is proved that, both in normed spaces and in simple metric spaces, the distances of sequences of points in adjacent subsets converge to the distance between such subsets under weak extra conditions compared to the cyclic contractive case, which is simply that the contractive constant be less than one. It is also proved that if the metric space is a uniformly convex Banach space and one of the involved subsets is convex then all the sequences between adjacent subsets converge to a unique set of best proximity points, one of them per subset which conform a limit cycle, although the sets of best proximity points are not all necessarily singletons in all the subsets. Full article
(This article belongs to the Topic Fixed Point Theory and Measure Theory)
28 pages, 516 KB  
Article
A Solution to the Non-Cooperative Equilibrium Problem for Two and Three Players Using the Fixed-Point Technique
by Muhammad Tariq, Sabeur Mansour, Mujahid Abbas and Abdullah Assiry
Symmetry 2025, 17(4), 544; https://doi.org/10.3390/sym17040544 - 2 Apr 2025
Cited by 1 | Viewed by 511
Abstract
The aims of this paper are (a) to introduce the concept of the 0-complete m-metric spaces, (b) to obtain the results for mw-Caristi mapping using Kirk’s approach, (c) to investigate the problem of non-cooperative equilibrium (abbreviated as NCE) in two- [...] Read more.
The aims of this paper are (a) to introduce the concept of the 0-complete m-metric spaces, (b) to obtain the results for mw-Caristi mapping using Kirk’s approach, (c) to investigate the problem of non-cooperative equilibrium (abbreviated as NCE) in two- and three-person games in the structure of game theory and find the solution by employing coupled and tripled fixed-point results within the framework of 0-complete m-metric spaces (m-metric spaces, respectively), and (d) to establish some coupled fixed-point results which extend the scope of metric fixed point theory. We provide some examples to support the concepts and results presented in this paper. As an application of our results in this paper, we obtain the existence of a solution for a nonlinear integral equation. Full article
(This article belongs to the Topic Fixed Point Theory and Measure Theory)
Show Figures

Figure 1

14 pages, 285 KB  
Article
Functional Variant of Polynomial Analogue of Gandy’s Fixed Point Theorem
by Andrey Nechesov and Sergey Goncharov
Mathematics 2024, 12(21), 3429; https://doi.org/10.3390/math12213429 - 31 Oct 2024
Cited by 2 | Viewed by 1429
Abstract
In this work, a functional variant of the polynomial analogue of Gandy’s fixed point theorem is obtained. Sufficient conditions have been found to ensure that the complexity of recursive functions does not exceed polynomial bounds. This opens up opportunities to enhance the expressivity [...] Read more.
In this work, a functional variant of the polynomial analogue of Gandy’s fixed point theorem is obtained. Sufficient conditions have been found to ensure that the complexity of recursive functions does not exceed polynomial bounds. This opens up opportunities to enhance the expressivity of p-complete languages by incorporating recursively defined constructs. This approach is particularly relevant in the following areas: AI-driven digital twins of smart cities and complex systems, trustworthy AI, blockchains and smart contracts, transportation, logistics, and aerospace. In these domains, ensuring the reliability of inductively definable processes is crucial for maintaining human safety and well-being. Full article
(This article belongs to the Topic Fixed Point Theory and Measure Theory)
Back to TopTop