Dear Colleagues,

Beginning almost a century ago, with the fixed-point theorem that Banach proved in his thesis, fixed point theory is a common cornerstone of applied mathematics, functional analysis, and topology. The result of Banach is an abstraction of the method of successive approximation that was used the solve certain differential equations by eminent mathematicians, such as Liouville and Picard and so on. In order words, metric fixed-point theory is applicable to real-world problems. Indeed, metric fixed-point theory has been efficiently used not only in various branches of mathematics, but also in almost all qualitative sciences, such as economics, theoretical computer science, biology, chemistry, and physics engineering.

In the past few decades, several interesting problems have been solved using fixed point theory. In addition to classical ordinary differential equations and integral equation, researchers also focus on fractional differential equations (FDE) and fractional integral equations (FIE). Indeed, FDE and FIE lead to a better understanding of several physical phenomena, which is why such differential equations have been highly appreciated and explored. We also note the importance of distinct abstract spaces, such as quasi-metric, b-metric, symmetric, partial metric, and dislocated metric. Sometimes, one of these spaces is more suitable for a particular application. Fixed point theory techniques in partial metric spaces have been used to solve classical problems of semantic and domain theory of computer science.

This Special Issue will collect ideas on theoretical advances in the metric fixed-point theory and possible applications (as mentioned above, on fractional differential/integral equations, semantic and domain theory, and so on). We welcome both original research articles and articles discussing the current situation. Potential issues include but are not limited to the following:

• Iterative fixed-point theory;
• Fixed point theory and applications;
• Best proximity point theory and applications;
• Recursive mappings and convergence;
• Good exposure and control in fixed point theory and FDE;
• Nonlinear problems with fixed point theory approaches.

Prof. Dr. Erdal Karapinar
Prof. Dr. Juan Martínez-Moreno
Prof. Dr. Inci M. Erhan
Guest Editors

Manuscript Submission Information

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• fixed point theory
• best proximity point theory
• recursive sequence
• quasi-metric
• b-metric spaces
• symmetric spaces
• dislocated metric spaces
• partial metric spaces
• semantic domain theory
• biological systems and bioinformatics