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Semicompatibility and fixed point theorems in an unbounded D -metric space

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  • Bijendra Singh
  • Shishir Jain
  • Shobha Jain

Abstract

Rhoades (1996) proved a fixed point theorem in a bounded D -metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unbounded D -metric space, for two self-maps satisfying a general contractive condition with a restricted domain of x and y . This has been done by using the notion of semicompatible maps in D -metric space. These results generalize and improve the results of Rhoades (1996), Dhage et al. (2000), and Veerapandi and Rao (1996). These results also underline the necessity and importance of semicompatibility in fixed point theory of D -metric spaces. All the results of this paper are new.

Suggested Citation

  • Bijendra Singh & Shishir Jain & Shobha Jain, 2005. "Semicompatibility and fixed point theorems in an unbounded D -metric space," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-13, January.
    • Handle: RePEc:hin:jijmms:576739
    DOI: 10.1155/IJMMS.2005.789
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    Cited by:

    1. Cho, Yeol Je & Sedghi, Shaban & Shobe, Nabi, 2009. "Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2233-2244.

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