Fixed Point Theory and Measure Theory

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

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
AppliedMath appliedmath	1.4	1.4	2021	20.4 Days	CHF 1200	Submit
Axioms axioms	1.5	-	2012	21.6 Days	CHF 2400	Submit
Fractal and Fractional fractalfract	3.5	6.8	2017	17.2 Days	CHF 2700	Submit
Mathematics mathematics	2.3	5.4	2013	17.4 Days	CHF 2600	Submit
Symmetry symmetry	2.2	5.2	2009	16.3 Days	CHF 2400	Submit

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Published Papers (11 papers)

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20 pages, 302 KB  

Open AccessArticle

New Refinements of the Generalized Versions of Hölder’s Inequality

by László Horváth

Symmetry 2026, 18(8), 1360; https://doi.org/10.3390/sym18081360 - 12 Aug 2026

Viewed by 173

Abstract

In this paper, we present new refinements of the generalized versions of Hölder’s inequality. Such refinements are rare. Our results are novel and clearly illustrate the essence of some recent specific refinements. As for applications, we present new inequalities for integral power means, [...] Read more.

In this paper, we present new refinements of the generalized versions of Hölder’s inequality. Such refinements are rare. Our results are novel and clearly illustrate the essence of some recent specific refinements. As for applications, we present new inequalities for integral power means, give a new refinement of the generalized Opial–Olech inequality, refine the well-known inequality between Rényi’s entropies with different parameters by utilizing the concept of “useful” information, and finally, we obtain a refinement of the Cauchy–Bunyakovsky–Schwarz inequality. Full article

(This article belongs to the Topic Fixed Point Theory and Measure Theory)

19 pages, 297 KB  

Open AccessArticle

α-η-ψ Contractions in Convex b-Metric Spaces: Fixed Point Results and Applications

by Gehad M. Abd-Elhamed and Afrah Al-Bossly

Mathematics 2026, 14(14), 2504; https://doi.org/10.3390/math14142504 - 11 Jul 2026

Viewed by 290

Abstract

A novel class of $\alpha$-$\eta$-$\psi$ contractions in complete convex b-metric spaces is introduced in this study. Using a generalized contractive framework, we establish existence and uniqueness results for fixed points. As applications, we explore the solvability of nonlinear integral [...] Read more.

A novel class of $\alpha$-$\eta$-$\psi$ contractions in complete convex b-metric spaces is introduced in this study. Using a generalized contractive framework, we establish existence and uniqueness results for fixed points. As applications, we explore the solvability of nonlinear integral equations, delay neural networks, and optimization problems. The applications and effectiveness of the theoretical findings are demonstrated by numerical examples. Full article

(This article belongs to the Topic Fixed Point Theory and Measure Theory)

18 pages, 1524 KB  

Open AccessArticle

Common Fixed Point Theorems for (β, α)-Generalized Enriched Contractions in Banach Spaces

by Rekha Panicker and Rahul Shukla

AppliedMath 2026, 6(6), 86; https://doi.org/10.3390/appliedmath6060086 - 2 Jun 2026

Viewed by 388

Abstract

This paper investigates common fixed point theorems for $(\beta ,\alpha )$-generalized enriched contractions in Banach spaces. We provide a corrected proof of an existing theorem on enriched contractions, thereby strengthening the reliability of results in this area. Our analysis further [...] Read more.

This paper investigates common fixed point theorems for $(\beta ,\alpha )$-generalized enriched contractions in Banach spaces. We provide a corrected proof of an existing theorem on enriched contractions, thereby strengthening the reliability of results in this area. Our analysis further shows that a previously published illustrative example does not satisfy the proposed enriched contraction condition, since the condition fails for $x=0, y=\frac{1}{8}$, and $b=\frac{4}{5}$. We then introduce a generalized pair of mappings and prove two common fixed point theorems for single-valued $(\beta ,\alpha )$-generalized enriched contractions under weak commutativity and compatibility conditions. Strong convergence to the unique common fixed point is established through a Mann-type iteration process, and an example is provided to validate the proposed generalizations. Full article

(This article belongs to the Topic Fixed Point Theory and Measure Theory)

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11 pages, 232 KB  

Open AccessArticle

Fixed Point Results for Large Closed Four-Step Orbital Contractions in Metric Spaces

by Nawal Alharbi

Mathematics 2026, 14(10), 1680; https://doi.org/10.3390/math14101680 - 14 May 2026

Viewed by 315

Abstract

This paper introduces a higher-order orbital framework in fixed point theory based on a closed four-step orbital functional. Existing approaches, such as triangle-perimeter contractions, mainly rely on three-point configurations and first-order geometric interactions. In contrast, the proposed functional incorporates four successive iterates together [...] Read more.

This paper introduces a higher-order orbital framework in fixed point theory based on a closed four-step orbital functional. Existing approaches, such as triangle-perimeter contractions, mainly rely on three-point configurations and first-order geometric interactions. In contrast, the proposed functional incorporates four successive iterates together with a nonlocal comparison term involving second-order orbital displacements. Using this structure, we define a new class of large closed four-step orbital contractions and establish a corresponding fixed point theorem in complete metric spaces under a boundedness assumption on one orbit. The proof is based on a propagation mechanism that transfers contractive behavior along the orbit generated by the mapping. Several examples demonstrate that the proposed framework extends classical contraction settings such as Banach and triangle-perimeter contractions. Furthermore, an application to a nonlinear Volterra integral equation provides explicit analytical estimates showing how the four-step orbital contraction structure can be verified in functional settings. These results provide a higher-order orbital extension of existing contraction principles and may contribute to further developments in generalized metric spaces and nonlinear analysis. Full article

(This article belongs to the Topic Fixed Point Theory and Measure Theory)

18 pages, 303 KB  

Open AccessArticle

Fixed Point Results in Convex Double-Controlled Metric-Type Spaces and Applications

by Nazli Kadioglu Karaca

Mathematics 2026, 14(10), 1620; https://doi.org/10.3390/math14101620 - 10 May 2026

Viewed by 312

Abstract

This paper investigates fixed point results in convex double-controlled metric-type spaces. By introducing a convex structure on double-controlled metric-type spaces, we study the convergence of the Mann iteration process for contractive mappings in this framework. Under suitable conditions on the control functions, we [...] Read more.

This paper investigates fixed point results in convex double-controlled metric-type spaces. By introducing a convex structure on double-controlled metric-type spaces, we study the convergence of the Mann iteration process for contractive mappings in this framework. Under suitable conditions on the control functions, we establish the existence and uniqueness of fixed points and prove that the Mann iterative sequence converges to the fixed point. In addition, we investigate the stability of the Mann iteration process and establish a data dependence result. Finally, an application to a Fredholm integral equation is presented to illustrate the applicability of the obtained results. Full article

(This article belongs to the Topic Fixed Point Theory and Measure Theory)

10 pages, 252 KB  

Open AccessArticle

Fixed-Point Results in Metric Spaces for Large Triangle–Perimeter Contractions

by Mouataz Billah Mesmouli, Loredana Florentina Iambor and Taher S. Hassan

Mathematics 2026, 14(3), 457; https://doi.org/10.3390/math14030457 - 28 Jan 2026

Cited by 2 | Viewed by 622

Abstract

We introduce a new class of mappings, referred to as large triangle–perimeter contractions, which simultaneously extend Petrov’s triangle–perimeter contractions and Burton’s large contraction principle. The proposed approach combines a strict local reduction of triangle perimeters with a nonuniform contractive mechanism that becomes effective [...] Read more.

We introduce a new class of mappings, referred to as large triangle–perimeter contractions, which simultaneously extend Petrov’s triangle–perimeter contractions and Burton’s large contraction principle. The proposed approach combines a strict local reduction of triangle perimeters with a nonuniform contractive mechanism that becomes effective whenever the underlying triangle is sufficiently nondegenerate. Within this two-scale setting, we establish a fixed-point theorem showing that every such mapping defined on a complete metric space admits a unique fixed point, provided that one orbit is bounded. The proof follows the spirit of Burton’s decay technique, adapted here to control the behavior of triangle perimeters rather than pairwise distances. Several illustrative examples, including both continuous and discrete cases, demonstrate that this class strictly contains mappings that fail to satisfy Petrov’s uniform perimeter contraction condition. Full article

(This article belongs to the Topic Fixed Point Theory and Measure Theory)

15 pages, 280 KB  

Open AccessArticle

On Ćirić-Type Fixed Point Results on Interpolative b-Metric Spaces with Application to Volterra Integral Equations

by Pradip Debnath and Nabanita Konwar

Symmetry 2025, 17(11), 1914; https://doi.org/10.3390/sym17111914 - 8 Nov 2025

Cited by 5 | Viewed by 1094

Abstract

This paper introduces a new class of generalized metric structures, called interpolative b-metric spaces, which unify and extend both b-metric spaces and interpolative metric spaces in a non-trivial way. By incorporating a nonlinear correction term alongside a multiplicative scaling parameter into [...] Read more.

This paper introduces a new class of generalized metric structures, called interpolative b-metric spaces, which unify and extend both b-metric spaces and interpolative metric spaces in a non-trivial way. By incorporating a nonlinear correction term alongside a multiplicative scaling parameter into the triangle inequality, this framework enables broader contractive conditions and refined control of convergence behavior. We develop the foundational theory of interpolative b-metric spaces and establish a generalized Ćirić-type fixed point theorem, along with Banach, Kannan, and Bianchini-type results as corollaries. To highlight the originality and applicability of our approach, we apply the main theorem to a nonlinear Volterra-type integral equation, demonstrating that interpolative b-metrics effectively accommodate nonlinear solution structures beyond the scope of traditional metric models. This work offers a unified platform for fixed point analysis and opens new directions in nonlinear and functional analysis. Full article

(This article belongs to the Topic Fixed Point Theory and Measure Theory)

8 pages, 235 KB  

Open AccessArticle

A Fixed-Point Chatterjea–Singh Mapping Approach: Existence and Uniqueness of Solutions to Nonlinear BVPs

by Zouaoui Bekri, Nicola Fabiano, Abdulaziz Khalid Alsharidi and Mohammed Ahmed Alomair

Mathematics 2025, 13(20), 3295; https://doi.org/10.3390/math13203295 - 15 Oct 2025

Cited by 1 | Viewed by 775

Abstract

This paper introduces an application of the Chatterjea–Singh fixed-point theorem to nonlinear boundary value problems (BVPs). We define a Chatterjea–Singh mapping as one whose iterate $T^p$ satisfies a Chatterjea-type contractive condition. Under this weaker assumption than classical Banach or Chatterjea contractions, we [...] Read more.

This paper introduces an application of the Chatterjea–Singh fixed-point theorem to nonlinear boundary value problems (BVPs). We define a Chatterjea–Singh mapping as one whose iterate $T^p$ satisfies a Chatterjea-type contractive condition. Under this weaker assumption than classical Banach or Chatterjea contractions, we prove the existence and uniqueness of solutions to second-order BVPs. Our method applies even when T itself does not satisfy a contraction property. Examples illustrate how iteration can recover convergence where standard conditions fail. This work extends generalized fixed-point theory in differential equations and highlights the flexibility of delayed contraction criteria. Full article

(This article belongs to the Topic Fixed Point Theory and Measure Theory)

17 pages, 344 KB  

Open AccessEditor’s ChoiceArticle

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

Cited by 2 | Viewed by 856

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 $p\ge 2$ 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 $p\ge 2$ 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  

Open AccessArticle

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 2 | Viewed by 932

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 $m^w$-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 $m^w$-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)

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14 pages, 285 KB  

Open AccessArticle

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 2070

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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