b-Metric Spaces

  • William Kirk
  • Naseer Shahzad


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.


Triangle Inequality Comparison Function Unique Fixed Point Quasimetric Space Picard Operator 
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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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