# A general fixed point theorem for pairs of weakly compatible mappings in G--metric spaces

Volume 5, Issue 2, pp 151--160 Publication Date: April 11, 2012
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### Authors

Valeriu Popa - Department of Mathematics, Informatics and Educational Sciences, Faculty of Sciences ''Vasile Alecsandri'' University of Bacău, 157 Calea Mărăşeşti, Bacău, 600115, Romania. Alina-Mihaela Patriciu - Department of Mathematics, Informatics and Educational Sciences, Faculty of Sciences ''Vasile Alecsandri'' University of Bacău, 157 Calea Mărăşeşti, Bacău, 600115, Romania.

### Abstract

In this paper a general fixed point theorem in G-metric spaces for weakly compatible mappings is proved, theorem which generalize the results from Abbas et. al. [M. Abbas and B. E. Rhoades, Appl. Math. and Computation 215 (2009), 262 - 269] and [M. Abbas, T. Nazir and S. Radanović, Appl. Math. and Computation 217 (2010), 4094 - 4099]. In the last part of this paper it is proved that the fixed point problem for these mappings is well posed.

### Keywords

• G-metric space
• weakly compatible mappings
• fixed point.

•  54H25
•  47H10

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