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On Fixed-Point Results in Controlled Partial Metric Type Spaces with a Graph

Author

Listed:
  • Nizar Souayah

    (Department of Natural Sciences, Community College Al-Riyadh, King Saud University, Riyadh 145111, Saudi Arabia)

  • Mehdi Mrad

    (Department of Industrial Ingeneering, College of engineering, King Saud University, Riyadh 145111, Saudi Arabia)

Abstract

Recently, Mlaiki et al. introduced the notion of a controlled metric type space which is a generalization of the b -metric space. In this work, we define the controlled partial metric type space and give some fixed-point theorems for extensions of Kannan contraction in this space with suitable conditions. Moreover, as an application, we derive a fixed-point theorem for graphic contraction on the considered metric space endowed with a graph.

Suggested Citation

  • Nizar Souayah & Mehdi Mrad, 2019. "On Fixed-Point Results in Controlled Partial Metric Type Spaces with a Graph," Mathematics, MDPI, vol. 8(1), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2019:i:1:p:33-:d:302383
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