On Ray's theorem for weak firmly nonexpansive mappings in Hilbert Spaces

Authors

  • Tamer Nabil
  • Ahmed Hussein Soliman Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt

DOI:

https://doi.org/10.24297/jam.v12i1.610

Keywords:

generalized firmly nonexpansive mapping, fundamentally firmly nonexpansive mapping, fixed point, Hilbert space., Ray's theorem

Abstract

In this work, we introduce notions of generalized firmly nonexpansive (G-firmly non expansive) and fundamentally firmly nonexpansive (F-firmly nonexpansive) mappings and utilize to the same to prove Ray's theorem for G-firmly and F-firmly nonexpansive mappings in Hilbert Spaces. Our results extend the result due to F. Kohsaka [ Ray's theorem revisited: a fixed point free firmly nonexpansive mapping in Hilbert spaces, Journal of Inequalities and Applications (2015) 2015:86 ].

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Author Biography

Tamer Nabil

Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt

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Published

2016-03-30

How to Cite

Nabil, T., & Soliman, A. H. (2016). On Ray’s theorem for weak firmly nonexpansive mappings in Hilbert Spaces. JOURNAL OF ADVANCES IN MATHEMATICS, 12(1), 5858–5861. https://doi.org/10.24297/jam.v12i1.610

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Articles