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
1784

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
- - 2021 25.3 Days CHF 1000 Submit
Axioms
axioms
1.9 - 2012 22.8 Days CHF 2400 Submit
Fractal and Fractional
fractalfract
3.6 4.6 2017 23.7 Days CHF 2700 Submit
Mathematics
mathematics
2.3 4.0 2013 18.3 Days CHF 2600 Submit
Symmetry
symmetry
2.2 5.4 2009 17.3 Days CHF 2400 Submit

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Published Papers (1 paper)

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14 pages, 285 KiB  
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 1049
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)
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