Research in Mathematics

Fixed Point Theory and Algorithms in Computational Mathematics

Fixed Point Theory and Contraction-based Algorithms constitute a fundamental pillar of modern applied mathematics, underpinning a wide range of theoretical and computational developments in nonlinear analysis. These methodologies play a crucial role in the study of nonlinear equations, optimization problems, variational inequalities, and dynamical systems. In recent years, the rapid growth of artificial intelligence, machine learning, and data-driven modelling has led to the emergence of intelligent computational frameworks that increasingly interact with classical mathematical principles. In particular, hybrid approaches that integrate fixed point algorithms with intelligent models have shown strong potential for enhancing convergence properties, robustness, and computational efficiency. This Special Issue focuses on the mathematical foundations, algorithmic structures, and practical implementations of fixed point methods and intelligent models, emphasizing their role in addressing complex problems arising in computational mathematics and related disciplines.

The increasing complexity of real-world systems in science, engineering, economics, and technology demands analytical tools that are both mathematically rigorous and computationally efficient. Fixed point algorithms provide powerful mechanisms for guaranteeing existence, uniqueness, and convergence in nonlinear problems, while intelligent models offer adaptability and scalability in high-dimensional and data-intensive environments. The integration of these two paradigms has become increasingly important for developing reliable solution frameworks capable of handling uncertainty, nonlinearity, and large-scale computation. Moreover, such hybrid methodologies contribute to bridging the gap between abstract mathematical theory and practical applications, enabling new insights into convergence analysis, stability, and optimization performance.

This Article Collection aims to advance rigorous mathematical theory while highlighting impactful applications supported by well-founded analytical and computational techniques. By bringing together advances in fixed point theory, contraction mappings, and intelligent computational models, this Article Collections aims to highlight contemporary mathematical techniques that respond to current scientific challenges and stimulate further interdisciplinary research.

We invite original research articles and high-quality review papers that align with the scope of Research in Mathematics and address theoretical, computational, and applied aspects of fixed-point theory and algorithms. Topics of interest include, but are not limited to:

• Generalized Contraction Mappings
• Fixed Point Iterative Schemes
• Optimization Methods
• Variational Inequality Problems
• Nonlinear Operator Equations
• Convergence Analysis

Particular emphasis is placed on applications where fixed-point methodologies play a central analytical or computational role, such as: equilibrium modelling in economics and game theory, stability analysis of dynamical and control systems, signal and image reconstruction, inverse problems, and numerical schemes for nonlinear partial and integral equations. Contributions integrating machine learning, artificial intelligence, or data-driven approaches with fixed point frameworks are especially encouraged, including applications in data assimilation, network dynamics, intelligent control, and large-scale optimization.

Keywords: Contraction Mappings, Variational Inequality Problems, Optimization and Nonlinear Analysis, AI-driven Mathematical Models, Intelligent and Fuzzy Systems

Manuscript Submissions:

Manuscript submission is open until 31st October 2026.

Please carefully review the journal scope and author submission instructions prior to submitting an abstract as it will be rejected if it does not fall within the scope of the journal.

All manuscripts submitted to this Article Collection will undergo desk assessment and peer-review as part of our standard editorial process. Manuscripts which do not fall within the scope of the journal will be rejected.

To submit your papers to this Article Collection, please:

1. Check "Yes" for the question, "Are you submitting your paper for a specific special issue or article collection?"
2. Select the relevant Article Collection from the drop-down menu under the question, "Fixed Point Theory and Algorithms in Computational Mathematics"

We are able to offer a 10% Discount to all authors, and have a limited number of 20% Discount codes only available for early submissions. It should be noted that discount codes must be entered in at the point of submission as they cannot be applied retroactively, nor can these be combined as only the higher valued discount would be applicable.

Please contact Christopher Montgomery, Commissioning Editor regarding details on obtaining your discount codes, and with any other queries for this Article Collection.

Article Collection Guest Advisors

Dr. Pradip Debnath is an Associate Professor of Mathematical Sciences at Tezpur University, India, recognized among the World’s Top 2% Scientists (Stanford–Elsevier, 2023–2024). A former Associate Editor of Heliyon (Elsevier), and current Associate Editor of Research in Mathematics (Taylor & Francis), he serves on editorial boards of Scientific Reports (Nature), PLOS ONE, and several others. Holding a Ph.D. from NIT Silchar, India, his research spans fixed point theory, functional analysis, and soft computing. He has 75+ publications, reviewed 480+ papers, authored 10 books (Springer, CRC Press, etc.), and collaborates globally. He also mentors Ph.D. scholars and has led UGC-funded research project in fixed point theory.

Dr. Wutiphol Sintunavarat received his B.Sc. and M.Sc. degrees in Mathematics from Thammasat University, Thailand, and his Ph.D. in Applied Mathematics from King Mongkut’s University of Technology Thonburi under the Science Achievement Scholarship of Thailand (SAST). He is currently an Associate Professor at Thammasat University and has been an invited researcher at institutions in South Korea and Turkey. His research interests focus on fixed point theory and its applications in nonlinear functional analysis. He has published more than 200 research articles in international journals and has received several national and international awards, including recognition as one of the World’s Top 2% Scientists by Stanford University.