Fixed Point Theory and Measure Theory

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