Common Fixed Point Results for Occasionally Weakly Compatible Maps in G-Symmetric Spaces

DOI: 10.4236/am.2014.54071   PDF   HTML   XML   4,308 Downloads   5,413 Views   Citations


The notion of a G-symmetric space is introduced and the common fixed points for some pairs of occasionally weakly compatible maps satisfying some contractive conditions in a G-symmetric space are proved. The results extend and improve some results in literature.

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Eke, K. and Olaleru, J. (2014) Common Fixed Point Results for Occasionally Weakly Compatible Maps in G-Symmetric Spaces. Applied Mathematics, 5, 744-752. doi: 10.4236/am.2014.54071.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Eke, K.S. and Olaleru, J.O. (2013) Some Fixed Point Results on Ordered G-Partial Metric Spaces. ICASTOR Journal of Mathematical Sciences, 7, 65-78.
[2] Cartan, E. (1929) Sur la Determination d’un Systeme Orthogonal Complet dans un Espace de Riemman Symetrique Clos. Rendiconti del Circolo Matematico di Palermo, 53, 217-252.
[3] Wilson, W.A. (1931) On Semi-Metric Spaces. American Journal of Mathematics, 53, 361-373.
[4] Hicks, T.I. and Rhoades, B.E. (1999) Fixed Point Theory in Symmetric Spaces with Applications to Probabilistic Spaces. Nonlinear Analysis, 36, 331-344.
[5] Mustafa, Z. and Sims, B. (2006) A New Approach to Generalized Metric Spaces. Journal of Nonlinear and Convex Analysis, 7, 289-297.
[6] Kannan, R. (1968) Some Results on Fixed Points. Bulletin Calcutta Mathematical Society, 10, 71-76.
[7] Jungck, G. (1976) Commuting Mappings and Fixed Points. American Mathematics Monthly, 73, 261-263.
[8] Sessa, S. (1982) On a Weak Commutativity Condition of Mappings in Fixed Point Considerations. Publications of Institutional Mathematics, 32, 149-153.
[9] Jungck, G. (1986) Compatible Mappings and Common Fixed Points. International Journal of Mathematics and Mathematical Science, 9, 771-779.
[10] Al-Thagafi, M.A. and Shahzad, N. (2008) Generalised I-Nonexpansive Selfmaps and Invariant Approximations. Acta Mathematica Sinica, 24, 867-876.
[11] Pant, R.P. (1998) Common Fixed Points of Four Maps. Bulletin Calcutta Mathematical Society, 90, 281-286.
[12] Aamri, M. and El Moutawakil, D. (2002) Some New Common Fixed Point Theorems under Strict Contractive Conditions. Journal Mathematical Analysis and Applications, 270, 181-188.
[13] Jungck, G. and Rhoades, B.E. (2006) Fixed Point Theorems for Occasionally Weakly Compatible Mappings. Fixed Point Theory, 7, 287-296.
[14] Imdad, M., Ali, J. and Khan, L. (2006) Coincidence and Fixed Points in Symmetric Spaces under Strict Contractions. Journal of Mathematical Analysis and Applications, 320, 352-360.
[15] Bhatt, A., Chandra, H. and Sahu, D.R. (2010) Common Fixed Point Theorems for Occasionally Weakly Compatible Mappings under Relaxed Conditions. Nonlinear Analysis, 73, 176-182.
[16] Abbas, M. and Rhoades, B.E. (2008) Common Fixed Point Theorems for Occasionally Weakly Compatible Mappings Satisfying a Generalized Contractive Condition. Mathematical Communication, 13, 295-301.

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