Research ArticleOpen AccessGoogle Scholar indexed
Four Mappings Satisfying Ψ-Contractive Type Condition and Having Unique Common Fixed Point on 2-Metric Spaces
Department of Mathematics, College of Science, Yanbian University, Yanji, China
Department of Mathematics, College of Science, Yanbian University, Yanji, China
- 1 Department of Mathematics, College of Science, Yanbian University, Yanji, China
- 2 Department of Mathematics, College of Science, Yanbian University, Yanji, China
Advances in Pure Mathematics·Volume 03 (2013)·Pages 277–281·Published 5 March 2013·DOI10.4236/apm.2013.32039
Copy link · social · email
Abstract
In this paper, we introduce a class Ψ of real functions defined on the set of non-negative real numbers, and obtain a new unique common fixed point theorem for four mappings satisfying Ψ-contractive condition on a non-complete 2-metric space and give the versions of the corresponding result for two and three mappings.
Keywords2-Metric SpaceClass ΨCauchy SequenceCoincidence PointCommon Fixed Point
- H. S. Yang and D. S. Xiong, “A Common Fixed Point Theorem on P-Metric Spaces,” Journal of Yunnan Normal University (Science Edition), Vol. 21, No. 1, 2001, pp. 9-12.
- S. L. Singh, “Some Contractive Type Principles on 2-Metric Spaces and Applications”, Mathematics Seminar Notes (Kobe University), Vol. 7, No. 1, 1979, pp. 1-11.
- Y. J. Piao and Y. F. Jin, “Unique Common Fixed Point Theorem for a Family of Contractive Type Non-Commuting Selfmaps in 2-Metric Spaces,” Journal of Yanbian University (Science Edition), Vol. 32, No. 1, 2006, pp. 1-3.
- Y. J. Piao, “A Family of Quasi-Contractive Type Non-Commutative Self-Maps Having an Unique Common Fixed Point in 2-Metric Spaces,” Journal of Heilongjiang University (Science Edition), Vol. 23, No. 5, 2006 pp. 655-657.
- Y. J. Piao, “Unique Common Fixed Point for a Family of Self-Maps with Same Type Contractive Condition in 2-Metric Spaces,” Analysis in Theory and Applications, Vol. 24, No. 4, 2008, pp. 316-320. doi:10.1007/s10496-008-0316-9
- Y. J. Piao, “Unique Common Fixed Point for a Family of Self-Maps with Same Quasi-Contractive Type Condition in 2-Metric Space,” Journal of Nanjing University (Mathematical Biquarterly), Vol. 27, No. 1, 2010, pp. 82-87.
- Y. J. Piao, “Uniqueness of Common Fixed Point for a Family of Mappings withφ-Contractive Condition in 2-Metric Space”, Applied Mathematics, Vol. 3, 2012, pp. 73-77. doi:10.4236/am.2012.31012
- Y. J. Piao and Y. F. Jin, “New Unique Common Fixed Point Results for Four Mappings withΦ-Contractive Type in 2-Metric Spaces,” Applied Mathematics, Vol. 3, 2012, pp. 734-737. doi:10.4236/am.2012.37108
- M. Abbas and G. Jungck, “Common Fixed Point Results for Noncommuting Mappings without Continuity in Cone Metric Spaces,” Journal of Mathematical Analysis and Applications, Vol. 341, No. 1, 2008, pp. 416-420. doi:10.1016/j.jmaa.2007.09.070
- Y. Han and S. Y. Xu, “New Common Fixed Point Results for Four Maps on Cone Metric Spaces,” Applied Mathematics, Vol. 2, 2011, pp.1114-1118. doi:10.4236/am.2011.29153
- C. D. Bari and P. Vetro, “Φ-Pairs and Common Fixed Points in Cone Metric Spaces,” Rendicontidel Circolo Matematico Palermo, Vol. 57, 2008, pp. 279-285.