A graphical version of Reich’s fixed point theorem

Monther R. Alfuraidan, Mostafa Bachar, Mohamed A. Khamsi

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In this paper, we discuss the definition of the Reich multivalued monotone contraction mappings defined in a metric space endowed with a graph. In our investigation, we prove the existence of fixed point results for these mappings. We also introduce a vector valued Bernstein operator on the space C([0, 1],X), where X is a Banach space endowed with a partial order. Then we give an analogue to the Kelisky-Rivlin theorem.

Original languageBritish English
Pages (from-to)3931-3938
Number of pages8
JournalJournal of Nonlinear Science and Applications
Issue number6
StatePublished - 2016


  • Fixed point theory
  • Graph theory
  • Multivalued monotone contraction
  • Partial order


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