Trends in Fixed Point Theory and Fractional Calculus
1. Introduction
2. Overview of the Published Papers
- Fixed-Point Theorems in Branciari Distance Spaces (Seong-Hoon Cho) introduces -Caristi and generalized -contraction maps, establishing fixed-point results that extend Caristi’s theorem and Banach’s contraction principle and clarifying the relationships among various contraction conditions.
- m-Isometric Operators with Null Symbol and Elementary Operator Entries (Bhagwati Prashad Duggal) investigates strict -isometric operator pairs on Banach spaces, offering structural insights relevant to functional analysis and operator theory.
- Relational Almost -Contractions and Applications to Nonlinear Fredholm Integral Equations (Fahad M. Alamrani et al.) presents new fixed-point results under relational strict almost -contractions, with applications to the solvability of nonlinear Fredholm integral equations.
- Fixed-Point Results of F-Contractions in Bipolar p-Metric Spaces (Nabanita Konwar and Pradip Debnath) develops Banach-type and Reich-type theorems for F-contractions in bipolar p-metric spaces, supported by illustrative examples.
- Fixed Point Results in Modular b-Metric-like Spaces with an Application (Nizamettin Ufuk Bostan and Banu Pazar Varol) introduces modular b-metric-like spaces, defines notions of -convergence and -Cauchy sequences, and proves fixed-point theorems with practical applications.
- Enriched Z-Contractions and Fixed-Point Results with Applications to IFS (Ibrahim Alraddadi et al.) initiates a broad class of enriched -contractions on Banach spaces, establishing uniqueness and existence theorems and applying them to iterative function systems.
- Nonlinear Contractions Employing Digraphs and Comparison Functions with an Application to Singular Fractional Differential Equations (Doaa Filali et al.) extends Jachymski’s contraction principle via digraphs to study fixed points in graph metric spaces, applying the results to singular fractional differential equations.
- Stability of Fixed Points of Partial Contractivities and Fractal Surfaces (María A. Navascués) examines a wide class of contractions in b-metric spaces, including Banach and Matkowski maps, providing convergence and stability results for Picard iterations with implications for fractal geometry.
- Three Existence Results in the Fixed Point Theory (Alexander J. Zaslavski) offers three new existence theorems for fixed points of nonexpansive and set-valued mappings, generalizing known results on F-contractions and set-valued contractions.
- Fixed-Point Results of Generalized -Contractive Mappings in Partially Ordered Controlled Metric Spaces with an Application to a System of Integral Equations (Mohammad Akram et al.) proves multiple fixed-point and coincidence point results, applying them to solve a system of integral equations.
3. Concluding Remarks
Conflicts of Interest
List of Contributions
- Cho, S.-H. Fixed-Point Theorems in Branciari Distance Spaces. Axioms 2025, 14, 635. https://doi.org/10.3390/axioms14080635.
- Duggal, B.P. m-Isometric Operators with Null Symbol and Elementary Operator Entries. Axioms 2025, 14, 503. https://doi.org/10.3390/axioms14070503.
- Alamrani, F.M.; Algehyne, E.A.; Alshaban, E.; Alatawi, A.; Mohammed, H.I.A.; Khan, F.A. Relational Almost -Contractions and Applications to Nonlinear Fredholm Integral Equations. Axioms 2025, 14, 1. https://doi.org/10.3390/axioms14010001.
- Konwar, N.; Debnath, P. Fixed-Point Results of F-Contractions in Bipolar p-Metric Spaces. Axioms 2024, 13, 773. https://doi.org/10.3390/axioms13110773.
- Bostan, N.U.; Varol, B.P. Fixed Point Results in Modular b-Metric-like Spaces with an Application. Axioms 2024, 13, 726. https://doi.org/10.3390/axioms13100726.
- Alraddadi, I.; Din, M.; Ishtiaq, U.; Akram, M.; Argyros, I.K. Enriched Z-Contractions and Fixed-Point Results with Applications to IFS. Axioms 2024, 13, 562. https://doi.org/10.3390/axioms13080562.
- Filali, D.; Dilshad, M.; Akram, M. Nonlinear Contractions Employing Digraphs and Comparison Functions with an Application to Singular Fractional Differential Equations. Axioms 2024, 13, 477. https://doi.org/10.3390/axioms13070477.
- Navascués, M.A. Stability of Fixed Points of Partial Contractivities and Fractal Surfaces. Axioms 2024, 13, 474. https://doi.org/10.3390/axioms13070474.
- Zaslavski, A.J. Three Existence Results in the Fixed Point Theory. Axioms 2024, 13, 425. https://doi.org/10.3390/axioms13070425.
- Akram, M.; Alshaikey, S.; Ishtiaq, U.; Farhan, M.; Argyros, I.K.; Regmi, S. Fixed-Point Results of Generalized -Contractive Mappings in Partially Ordered Controlled Metric Spaces with an Application to a System of Integral Equations. Axioms 2024, 13, 415. https://doi.org/10.3390/axioms13060415.
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Damjanović, B.; Debnath, P. Trends in Fixed Point Theory and Fractional Calculus. Axioms 2025, 14, 660. https://doi.org/10.3390/axioms14090660
Damjanović B, Debnath P. Trends in Fixed Point Theory and Fractional Calculus. Axioms. 2025; 14(9):660. https://doi.org/10.3390/axioms14090660
Chicago/Turabian StyleDamjanović, Boško, and Pradip Debnath. 2025. "Trends in Fixed Point Theory and Fractional Calculus" Axioms 14, no. 9: 660. https://doi.org/10.3390/axioms14090660
APA StyleDamjanović, B., & Debnath, P. (2025). Trends in Fixed Point Theory and Fractional Calculus. Axioms, 14(9), 660. https://doi.org/10.3390/axioms14090660