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Common Fixed Point Results for Occasionally Weakly Compatible Maps in G-Symmetric Spaces
Department of Computer and Information Science/Mathematics, Covenant University, Ota, Nigeria
Department of Mathematics, University of Lagos, Lagos, Nigeria
- 1 Department of Computer and Information Science/Mathematics, Covenant University, Ota, Nigeria
- 2 Department of Mathematics, University of Lagos, Lagos, Nigeria
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Abstract
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.
KeywordsCommon Fixed PointsGeneralized Contractive MappingsOccasionally Weakly Compatible MapsCompatible Maps(E-A) PropertyG-Symmetric Spaces
- 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.
- 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. http://dx.doi.org/10.1007/BF03024106
- Wilson, W.A. (1931) On Semi-Metric Spaces. American Journal of Mathematics, 53, 361-373. http://dx.doi.org/10.2307/2370790
- Hicks, T.I. and Rhoades, B.E. (1999) Fixed Point Theory in Symmetric Spaces with Applications to Probabilistic Spaces. Nonlinear Analysis, 36, 331-344. http://dx.doi.org/10.1016/S0362-546X(98)00002-9
- Mustafa, Z. and Sims, B. (2006) A New Approach to Generalized Metric Spaces. Journal of Nonlinear and Convex Analysis, 7, 289-297.
- Kannan, R. (1968) Some Results on Fixed Points. Bulletin Calcutta Mathematical Society, 10, 71-76.
- Jungck, G. (1976) Commuting Mappings and Fixed Points. American Mathematics Monthly, 73, 261-263. http://dx.doi.org/10.2307/2318216
- Sessa, S. (1982) On a Weak Commutativity Condition of Mappings in Fixed Point Considerations. Publications of Institutional Mathematics, 32, 149-153.
- Jungck, G. (1986) Compatible Mappings and Common Fixed Points. International Journal of Mathematics and Mathematical Science, 9, 771-779. http://dx.doi.org/10.1155/S0161171286000935
- Al-Thagafi, M.A. and Shahzad, N. (2008) Generalised I-Nonexpansive Selfmaps and Invariant Approximations. Acta Mathematica Sinica, 24, 867-876. http://dx.doi.org/10.1007/s10114-007-5598-x
- Pant, R.P. (1998) Common Fixed Points of Four Maps. Bulletin Calcutta Mathematical Society, 90, 281-286.
- 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. http://dx.doi.org/10.1016/S0022-247X(02)00059-8
- Jungck, G. and Rhoades, B.E. (2006) Fixed Point Theorems for Occasionally Weakly Compatible Mappings. Fixed Point Theory, 7, 287-296.
- 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. http://dx.doi.org/10.1016/j.jmaa.2005.07.004