An Improvement of a Known Unique Common Fixed Point Result for Four Mappings on 2-Metric Spaces

ABSTRACT

In this paper, we introduce a new class Γ, which is weak than a known class Ψ, of real continuous functions defined on [0, +∞), and use another method to prove the known unique common fixed point theorem for four mappings with *γ*-contractive condition instead of *Ψ*-contractive condition on 2-metric spaces.

Cite this paper

A. Jin and Y. Piao, "An Improvement of a Known Unique Common Fixed Point Result for Four Mappings on 2-Metric Spaces,"*Applied Mathematics*, Vol. 4 No. 11, 2013, pp. 1-5. doi: 10.4236/am.2013.411A1001.

A. Jin and Y. Piao, "An Improvement of a Known Unique Common Fixed Point Result for Four Mappings on 2-Metric Spaces,"

References

[1] H. L. Jin and Y. J. Piao, “Four Mappings Satisfying Ψ-Contractive Type Condition and Having Unique Common Fixed Point on 2-Metric Spaces ,” Advances in Pure Mathematics, Vol. 3, No. 2, 2013, pp. 277-281.

http://dx.doi.org/10.4236/apm.2013.32039

[2] B. Samet, M. Rajovic, R. Lazovi and R. Stoilikovic, “Common Fixed Point Results for Nonlinear Contractions in Ordered Partial Metric Spaces,” Fixed Point and Applications, Vol. 71, No. 1, 2011.

http://dx.doi.org/10.1186/1687-1812-2011-71

[3] 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.

[4] 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.

[5] 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.

http://dx.doi.org/10.1007/s10496-008-0316-9

[6] 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.

[7] 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.

http://dx.doi.org/10.1016/j.jmaa.2007.09.070

[8] Y. Han and S. Y. Xu, “New Common Fixed Point Results for Four Maps on Cone Metric Spaces,” Applied Mathematics, Vol. 2, No. 9, 2011, pp. 1114-1118.

http://dx.doi.org/10.4236/am.2011.29153

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

[1] H. L. Jin and Y. J. Piao, “Four Mappings Satisfying Ψ-Contractive Type Condition and Having Unique Common Fixed Point on 2-Metric Spaces ,” Advances in Pure Mathematics, Vol. 3, No. 2, 2013, pp. 277-281.

http://dx.doi.org/10.4236/apm.2013.32039

[2] B. Samet, M. Rajovic, R. Lazovi and R. Stoilikovic, “Common Fixed Point Results for Nonlinear Contractions in Ordered Partial Metric Spaces,” Fixed Point and Applications, Vol. 71, No. 1, 2011.

http://dx.doi.org/10.1186/1687-1812-2011-71

[3] 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.

[4] 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.

[5] 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.

http://dx.doi.org/10.1007/s10496-008-0316-9

[6] 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.

[7] 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.

http://dx.doi.org/10.1016/j.jmaa.2007.09.070

[8] Y. Han and S. Y. Xu, “New Common Fixed Point Results for Four Maps on Cone Metric Spaces,” Applied Mathematics, Vol. 2, No. 9, 2011, pp. 1114-1118.

http://dx.doi.org/10.4236/am.2011.29153

[9] C. D. Bari and P. Vetro, “