Research Article
A New Discussion on Banach-Type Fixed Point Result in Double-Composed Metric Spaces
Issue:
Volume 9, Issue 2, December 2025
Pages:
26-30
Received:
4 September 2025
Accepted:
30 September 2025
Published:
30 October 2025
DOI:
10.11648/j.engmath.20250902.11
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Abstract: One of the important research directions of fixed point theory is the generalization of metric spaces. An interesting generalization of metric space is the modification of triangular inequality. In the last few decades, many generalizations of metric space have been introduced in the field of fixed point theory by changing triangle inequality using multiplication of constants or functions. Recently, a new generalization of metric space with changing triangle inequality using the composition of two functions, namely, a double-composed metric space, has been introduced. A double-composed metric space is a new concept using the composition of functions, unlike the previous generalizations of metric space that modify the triangular inequality using the multiplication of functions. And, Banach-type fixed point result and Kanan-type fixed point result are established under certain assumptions in the setting of double-composed metric spaces. In this paper, we reconsider the Banach-type fixed point result in the setting of double-composed metric spaces under new and simple conditions. We have proved the fixed point theorem by using a new proof method and, consequently, we have demonstrated that Banach’s contractions in double-composed metric spaces have a unique fixed point under different assumptions from the previous one. We also present an example showing the validity of our fixed point result. Finally, we apply our fixed point result to show the existence of solution of Fredholm integral equations.
Abstract: One of the important research directions of fixed point theory is the generalization of metric spaces. An interesting generalization of metric space is the modification of triangular inequality. In the last few decades, many generalizations of metric space have been introduced in the field of fixed point theory by changing triangle inequality using...
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,
Gum-Sik Kang
