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Graphic Contraction Principle and Applications

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Mathematical Analysis and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 154))

Abstract

The purpose of this paper is to emphasize the role of the graphic contractions in metric fixed point theory. Two general results about the fixed points of graphic contractions and several related examples are given. The case of non-self graphic contractions will be also considered. Existence, uniqueness, data dependence, well-posedness, Ulam-Hyers stability, and the Ostrowski property for the fixed point equation will be discussed. Some fixed point results in metric spaces endowed with a partial ordering will be also proved. Finally, open questions and research directions are presented.

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Authors and Affiliations

  1. Department of Mathematics, Babeş-Bolyai University of Cluj-Napoca, Cluj-Napoca, Romania

    A. Petruşel & I. A. Rus

Authors
  1. A. Petruşel
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  2. I. A. Rus
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Correspondence to A. Petruşel .

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Editors and Affiliations

  1. Department of Mathematics, Zografou Campus, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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Petruşel, A., Rus, I.A. (2019). Graphic Contraction Principle and Applications. In: Rassias, T., Pardalos, P. (eds) Mathematical Analysis and Applications. Springer Optimization and Its Applications, vol 154. Springer, Cham. https://doi.org/10.1007/978-3-030-31339-5_15

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