Double-Composed Metric Spaces

Irshad Ayoob, Ng Zhen Chuan and Nabil Mlaiki ()
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Irshad Ayoob: Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
Ng Zhen Chuan: School of Mathematics, Universiti Sains Malaysia, Gelugor 11800, Penang, Malaysia
Nabil Mlaiki: Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia

Mathematics, 2023, vol. 11, issue 8, 1-12

Abstract: The double-controlled metric-type space ( X , D ) is a metric space in which the triangle inequality has the form D ( η , μ ) ≤ ζ 1 ( η , θ ) D ( η , θ ) + ζ 2 ( θ , μ ) D ( θ , μ ) for all η , θ , μ ∈ X . The maps ζ 1 , ζ 2 : X × X → [ 1 , ∞ ) are called control functions. In this paper, we introduce a novel generalization of a metric space called a double-composed metric space, where the triangle inequality has the form D ( η , μ ) ≤ α D ( η , θ ) + β D ( θ , μ ) for all η , θ , μ ∈ X . In our new space, the control functions α , β : [ 0 , ∞ ) → [ 0 , ∞ ) are composed of the metric D in the triangle inequality, where the control functions ζ 1 , ζ 2 : X × X → [ 1 , ∞ ) in a double-controlled metric-type space are multiplied with the metric D . We establish some fixed-point theorems along with the examples and applications.

Keywords: b-metric spaces; controlled metric spaces; double-controlled metric-type spaces; fixed point; double-composed metric spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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