Journal of Fixed Point Theory and Applications

, Volume 17, Issue 3, pp 455–475 | Cite as

Generalized metric spaces: A survey

Article

Abstract

Banach’s contraction mapping principle is remarkable in its simplicity, yet it is perhaps the most widely applied fixed point theorem in all of analysis with special applications to the theory of differential and integral equations. Because the underlined space of this theorem is a metric space, the theory that developed following its publication is known as the metric fixed point theory. Over the last one hundred years, many people have tried to generalize the definition of a metric space. In this paper, we survey the most popular generalizations and we discuss the recent uptick in some generalizations and their impact in metric fixed point theory.

Mathematics Subject Classification

Primary 47H09 Secondary 46B20 47H10 47E10 

Keywords

Banach contraction principle cone metric spaces fixed point generalized metric spaces Menger spaces b-metric spaces G-metric spaces modular metric spaces partially ordered metric spaces 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of Mathematical ScienceThe University of Texas at El PasoEl PasoUSA
  2. 2.Department of Mathematics and StatisticsKing Fahd University of Petroleum & MineralsDhahranSaudi Arabia

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