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b-Metric Spaces

  • William Kirk
  • Naseer Shahzad
Chapter

Abstract

In 1993 another axiom for semimetric spaces, which is weaker than the triangle inequality, was put forth by Czerwik [58] with a view of generalizing the Banach contraction mapping theorem. This same relaxation of the triangle inequality is also discussed in Fagin et al. [79], who call this new distance measure nonlinear elastic matching (NEM). The authors of that paper remark that this measure has been used, for example, in [55] for trademark shapes and in [153] to measure ice floes. Later Q.

Keywords

Triangle Inequality Comparison Function Unique Fixed Point Quasimetric Space Picard Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • William Kirk
    • 1
  • Naseer Shahzad
    • 2
  1. 1.Department of MathematicsUniversity of IowaIowa CityUSA
  2. 2.Department of MathematicsKing Abdulaziz UniversityJeddahSaudi Arabia

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