The fixed point theory provides a very powerful tool in mathematics and many other scientific fields such as nonlinear analysis, integral equations and differential equations. What is interesting in a recent study on the fixed point theory is the generalization of metric space (MS).
By generalizing the concept of MS in the fixed point theory, many mathematicians presented new concepts such as b-metric space, triple controlled metric type space and triple-composed metric space. Some other authors defined a new notion called S-metric space (S-MS). Later, some mathematicians introduced new concepts for generalizing S-MS by using the ideas of earlier space concepts. Sb-MS and triple controlled S-metric type space (TC-S-MTS) are typical examples.
Kil Chol Jin, a lecturer at the Faculty of Applied Mathematics, proposed a new concept of triple-composed S-metric space (TCS-MS). He got motivation from the concepts of TCMS and S-MS while analyzing the recent research results on S-MS.
TCS-MS is a new concept that uses the composition of three functions rather than the multiplication of three functions, unlike the recently introduced TC-S-MTS.
He presented some meaningful examples showing that triple-composed S-metric space is a real generalization of S-metric space and Sb-metric space. In addition, he proved a fixed point result for Proinov-type contractive mappings in triple-composed S-metric spaces.
For more information, please refer to his paper “Triple-Composed S-Metric Spaces and Related Fixed Point Results” in “Proceedings of KUTIC-2025”.