Banach’s contraction principle, which holds an important position in the fixed point theory, has been extended in two directions; one is the generalization of metric spaces (MS), and the other is the change of contraction conditions.
Recently, a new generalization of MS called DCMS has been introduced. The concept of F-contraction, first proposed by a researcher in 2012, has become an important generalization of Banach’s contraction mapping. Since then, many authors have further investigated his result, suggesting various extensions and modifications. They first presented results that underwent change or omission of some of the three conditions for the mapping F.
Kil Chol Jin, a researcher at the Faculty of Applied Mathematics, has investigated the generalization of DCMS using a previous researcher’s idea.
First, he defined a new space, namely, triplecomposed metric space (TCMS), by combining the properties of RMS and DCMS. He formed TCMS by using the composition of three functions in a quadrilateral inequality. Second, he presented fixed point results for nonlinear FT-contractions using only (F1) in TCMS. Finally, he led the obtained results to the application of nonlinear integral equations.
You can find details in his paper “Triple-Composed Metric Spaces and Related Fixed Point Results With Application” in “Journal of Function Spaces” (SCI).
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