New Unique Common Fixed Point Results for Four Mappings with Ф-Contractive Type in 2-Metric Spaces

ABSTRACT

In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on non-complete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. The main results generalize and improve many well-known and corresponding conclusions in the literatures.

In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on non-complete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. The main results generalize and improve many well-known and corresponding conclusions in the literatures.

Cite this paper

Y. Piao and Y. Jin, "New Unique Common Fixed Point Results for Four Mappings with Ф-Contractive Type in 2-Metric Spaces,"*Applied Mathematics*, Vol. 3 No. 7, 2012, pp. 734-737. doi: 10.4236/am.2012.37108.

Y. Piao and Y. Jin, "New Unique Common Fixed Point Results for Four Mappings with Ф-Contractive Type in 2-Metric Spaces,"

References

[1] Y. J. Piao, G. Z. Jin and B. J. Zhang, “A Family of Selfmaps Having an Unique Common Fixed Point in 2-Metric Spaces,” Journal of Yanbian University (Science Edition), Vol. 28, No. 1, 2002, pp. 1-5.

[2] 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.

[3] S. L. Singh,, “Some Contractive Type Principles on 2Metric Spaces and Applications,” Mathematics Seminar Notes (Kobe University), Vol. 7, No. 1, 1979, pp. 1-11.

[4] 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 (in Chinese).

[5] Y. J. Piao, “A Family of Quasi-Contractive Type NonCommutative 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 (in Chinese).

[6] Y. J. Piao, “Unique Common Fixed Point for a Family of Self-Maps with Same Type Contractive Condition in 2Metric Spaces,” Analysis in Theory and Applications, Vol. 24, No. 4, 2008, pp. 316-320. doi:10.1007/s10496-008-0316-9

[7] 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 (in Chinese).

[8] Y. J Piao, “Uniqueness of Common Fixed Point for a Family of Mappings with -Contractive Condition in 2Metric Spaces,” Applied Mathematics, Vol. 3, 2012, pp. 73-77. doi:10.4236/am.2012.31012

[9] 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

[10] 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

[11] C. D. Bari and P. Vetro, “ -Pairs and Common Fixed Points in Cone Metric Spaces,” Rendiconti del Circolo Matematico Palermo, Vol. 57, 2008, pp. 279-285.

[1] Y. J. Piao, G. Z. Jin and B. J. Zhang, “A Family of Selfmaps Having an Unique Common Fixed Point in 2-Metric Spaces,” Journal of Yanbian University (Science Edition), Vol. 28, No. 1, 2002, pp. 1-5.

[2] 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.

[3] S. L. Singh,, “Some Contractive Type Principles on 2Metric Spaces and Applications,” Mathematics Seminar Notes (Kobe University), Vol. 7, No. 1, 1979, pp. 1-11.

[4] 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 (in Chinese).

[5] Y. J. Piao, “A Family of Quasi-Contractive Type NonCommutative 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 (in Chinese).

[6] Y. J. Piao, “Unique Common Fixed Point for a Family of Self-Maps with Same Type Contractive Condition in 2Metric Spaces,” Analysis in Theory and Applications, Vol. 24, No. 4, 2008, pp. 316-320. doi:10.1007/s10496-008-0316-9

[7] 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 (in Chinese).

[8] Y. J Piao, “Uniqueness of Common Fixed Point for a Family of Mappings with -Contractive Condition in 2Metric Spaces,” Applied Mathematics, Vol. 3, 2012, pp. 73-77. doi:10.4236/am.2012.31012

[9] 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

[10] 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

[11] C. D. Bari and P. Vetro, “ -Pairs and Common Fixed Points in Cone Metric Spaces,” Rendiconti del Circolo Matematico Palermo, Vol. 57, 2008, pp. 279-285.