Quadruple Fixed Point of Multivalued Nonlinear Contraction Mappings

Article Sidebar

PDF
Cite as:
Animesh Gupta, R.N. Yadava, S.S. Rajput, Quadruple Fixed Point of Multivalued Nonlinear Contraction Mappings, Int. J. Anal. Appl., 4 (2) (2014), 87-99.

Main Article Content

Animesh Gupta, R.N. Yadava, S.S. Rajput

Abstract

The notion of Quadruple fixed point is introduced by Karapinar E. [6]. Samet and Vetro [12] established some coupled fixed point theorems for multivalued non linear contraction mapping in partially ordered metric spaces. In this paper, we obtain existence of quadrupled fixed point of multivalued nonlinear contraction mappings in framework work of partially ordered metric spaces. Also, we give an example.

Article Details

References

  1. Beg, I, Butt, AR: Coupled fixed points of set valued mappings in partially ordered metric spaces. J Nonlinear Sci Appl. 3, 179-185 (2010)
  2. Ciric, LjB: Multi-valued nonlinear contraction mappings. Nonlinear Anal. 71, 2716-2723 (2009). doi:10.1016/j. na.2009.01.116
  3. Ciric, LjB: Fixed point theorems for multi-valued contractions in complete metric spaces. J Math Anal Appl. 348, 499-507 (2008). doi:10.1016/j.jmaa.2008.07.062
  4. Du, WS: Coupled fixed point theorems for nonlinear contractions satisfied MizoguchiTakahashis condition in quasiordered metric spaces. Fixed Point Theory Appl. 9 (2010). 2010, Article ID 876372
  5. Hussain, N, Shah, MH, Kutbi, MA: Coupled coincidence point theorems for nonlinear contractions in partially ordered quasi-metric spaces with a Q-function. Fixed Point Theory Appl. 21 (2011). 2011, Article ID 703938
  6. Karapiner E., Quadruple Fixed Point Theorems for Weak φ- Contraction, ISRN Math. Anal. (2011), ID 989423, 15 pages, doi:10.5402/2011/989423.
  7. Mizoguchi, N, Takahashi, W: Fixed point theorems for multivalued mappings on complete metric spaces. J Math Anal Appl. 141, 177-188 (1989). doi:10.1016/0022-247X(89)90214-X
  8. Nadler, SB: Multivalued contraction mappings. Pacific J Math. 30, 475-488 (1969)
  9. Nieto, JJ, Rodriguez-Lopez, R: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order. 22, 223-239 (2005)
  10. Nieto, JJ, Rodriguez-Lopez, R: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations. Acta Math Sin (Engl Ser). 23, 2205- 2212 (2007). doi:10.1007/s10114-005-0769-0
  11. Nieto, JJ, Pouso, RL, Rodriguez-Lopez, R: Fixed point theorems in ordered abstract spaces. Proc Am Math Soc. 135, 2505-2517 (2007). doi:10.1090/S0002-9939-07-08729-1
  12. Samet, B, Vetro, C: Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces. Nonlinear Anal. 74, 4260-4268 (2011). doi:10.1016/j.na.2011.04.007