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Implicit Contractive Maps in Ordered Metric Spaces

In: Topics in Mathematical Analysis and Applications

Author

Listed:
  • Mihai Turinici

    (“A. Mylle” Mathematical Seminar, “A. I. Cuza” University)

Abstract

In Part 1, we show that most of the implicit contractions introduced by Wardowski [Fixed Point Theory Appl., 2012, 2012:94] are Matkowski type contractions. In Part 2, some limit type extensions are obtained for the fixed point result (involving implicit contractions) due to Altun and Simsek [Fixed Point Theory Appl., Volume 2010, Article ID 621469]. Moreover, the connections with a lot of related statements in the area due to Agarwal, El-Gebeily, and O’Regan [Appl. Anal. 87:109–116, 2008] are also discussed. Finally, in Part 3, a non-limit counterpart of these results is given, under the same general context.

Suggested Citation

  • Mihai Turinici, 2014. "Implicit Contractive Maps in Ordered Metric Spaces," Springer Optimization and Its Applications, in: Themistocles M. Rassias & László Tóth (ed.), Topics in Mathematical Analysis and Applications, edition 127, pages 715-746, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-06554-0_32
    DOI: 10.1007/978-3-319-06554-0_32
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