Recent Advances in Fixed Point Theory and Optimization Methods: Algorithms, Convergence Analysis, and Applications

Dear Colleagues,

Fixed point theory and contraction-based iterative methods form a fundamental pillar of modern applied mathematics and nonlinear analysis. They provide essential theoretical and computational tools for studying nonlinear equations, optimization problems, variational inequalities, equilibrium systems, and dynamical processes. Over the past decades, these methods have played a central role in establishing existence, uniqueness, and convergence results across a wide range of mathematical models.

In recent years, rapid progress in artificial intelligence, machine learning, and data-driven modelling has led to the emergence of hybrid computational frameworks that integrate classical fixed point theory with intelligent and adaptive algorithms. Such approaches have demonstrated significant potential for improving convergence behaviour, numerical stability, and computational efficiency, particularly in large-scale and high-dimensional problems. The interaction between fixed point methods and intelligent computational techniques is becoming increasingly important for addressing uncertainty, nonlinearity, and data-intensive structures in modern scientific and engineering applications.

This Special Issue aims to advance both the theoretical foundations and computational methodologies of fixed point theory and optimization. It places particular emphasis on algorithmic innovation, convergence analysis, and real-world applications, with the goal of bridging abstract mathematical theory and practical computational frameworks. By bringing together recent developments in fixed point theory, contraction mappings, and modern optimization techniques, this Special Issue seeks to highlight emerging mathematical tools that address contemporary challenges in science and engineering and to stimulate further interdisciplinary research.

We invite original research articles and high-quality review papers that contribute to the advancement of fixed point theory, contraction principles, and optimization algorithms, including their applications in computational and applied mathematics. Topics of interest include, but are not limited to, the following:

• Generalized contraction mappings and nonlinear operator theory
• Fixed point iterative algorithms and splitting methods
• Optimization and variational inequality problems
• Monotone operator theory and nonlinear equations
• Convergence analysis and stability of iterative schemes
• Numerical methods for differential and integral equations

Special emphasis will be placed on applications where fixed point methodologies play a central role, including equilibrium problems in economics and game theory, dynamical systems and control theory, signal and image processing, inverse problems, and numerical schemes for partial and integral differential equations.

Contributions that integrate fixed point theory with machine learning, artificial intelligence, and data-driven modelling are particularly encouraged. Such hybrid approaches include applications in data assimilation, network dynamics, intelligent control systems, and large-scale optimization problems arising in modern scientific and engineering contexts.

Dr. Austine Efut Ofem
Prof. Dr. Seithuti Philemon Moshokoa
Dr. Prasit Cholamjiak
Guest Editors

Manuscript Submission Information

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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-anonymized 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 semimonthly 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 2600 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.

• generalized contraction mappings and nonlinear operator theory
• fixed point iterative algorithms and splitting methods
• optimization and variational inequality problems
• monotone operator theory and nonlinear equations
• convergence analysis and stability of iterative schemes
• numerical methods for differential and integral equations