Common Fixed Point Theorems in Dislocated Cone Metric Spaces

Main Article Content

Ashok Kumar Goyal
Neelmani Gupta

Abstract

Jungck and Rhoades [20] introduced the notion of weakly compatible mappings, which is weaker than compatibility. Many interesting fixed point theorems for weakly compatible maps satisfying contractive type conditions have been obtained by various authors. In this paper, notion of dislocated cone is introduced and a common fixed point theorem for three pairs of weakly compatible mappings satisfying a rational inequality without any continuity requirement which generalize several previously known results due to Imdad and Ali [15], Goyal ([6], [7]), Goyal and Gupta ([8], [9]), Imdad-Khan [16], Jeong-Rhoades [17] and others.


 2010 Mathematical Sciences Classification: 54H25, 47H10

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Article Details

How to Cite
Goyal, A. K., & Gupta, N. . (2018). Common Fixed Point Theorems in Dislocated Cone Metric Spaces. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 9(3), 1424–1432. https://doi.org/10.61841/turcomat.v9i3.14695
Section
Research Articles

References

[ 1 ]Abbas, M. and Jungck, G., “Common fixed point results for non commuting mappings without continuity in cone

metric spaces”, J. Math. Anal. Appl., 341(1)(2008), 416–420.

[ 2 ]Abbas, M. and Rhoades, B.E., “Fixed and periodic results in cone metric spaces”, Applied Mathematics Letters,

(4)(2009), 511–515.

[ 3 ] Frechet, M., “Sur quelques points du calcul fonctionnnel”, Rend. Circ. Mat. Palermo, 22(1906), 1–74.

[ 4 ] Goyal, A. K., “Common fixed point theorem for six mappings in complete metric spaces”, Bull. Pure Appl.

Math., 3 (1)(2009), 24–35.

[ 5 ] Goyal, A. K., “Common fixed point theorems for weakly compatible mappings satisfying rational contractive

conditions”, International Journal of Psychosocial Rehabilitation, 17(1)(2013),138-145.

[ 6 ] Goyal, A. K. and Gupta Neelmani., “Common fixed point theorem for six mappings in cone metric spaces”,

BioGecko, 4(2)(2015), 7–16.

[ 7 ] Goyal, A. K. and Gupta Neelmani., “Common fixed point theorem for compatible mappings with the generalized

contractive mappings in cone metric spaces”,BioGecko, 5 (1)(2016), 16–26.

[ 8 ] Han, Y. and Xu, S., “Some fixed point theorems for expanding mappings without continuity in cone metric

spaces”, Fixed Point Theory Appl., 3(2013), 1–9.

[ 9 ] Huang, G. and Zhang, X., “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal.

Appl., 332(2007),1468–1476.

[ 10 ] Hitzler,P., “Generalized Metrics and Topology in Logic Programming Semantics”, Ph.D. Thesis National

University of Ireland, University College Cork,, 2001.

[ 11 ]Hitzler, P. and Seda, A.K., “Dislocated Topologies. Journal of Electrical Engineering”,51(2000), 3-7.

[ 12 ] IIic, D. and Rakocevic, V., “Common fixed points for maps on cone metric spaces”, J. Math. Anal. Appl.,

(2)(2008),876–882.

[ 13 ] Imdad, M. and Ali, J., “Pairwise coincidentally commuting mappings satisfying a rational inequality”, Italian

Journal of Pure and Applied Mathematics, 20(2006), 87-96.

[ 14 ] Imdad, M. and Khan, Q.H., “Six mappings satisfying a rational inequality”, Radovi Matematicki, 9(1999),

–260,.

[ 15 ] Jeong G.S. and Rhoades B.E.., “Some remarks for improving fixed point theorem for more than two maps”, Ind.

J. Pure. Appl. Math 28 (9) (1997), 1177-1196.

[ 16 ] Jungck G., “Commuting mappings and fixed points”, Amer. Math. Monthly., 83 (1976), 261-263.

[ 17 ] Jungck, G., Compatible mappings and common fixed point, Internet. J. Math and Math. Sci., 9 (4) (1986),

-779.

[ 18 ] Jungck, G. and Rhoades, B.E., “Fixed point for set valued function without continuity”, Ind. J. Pure. Appl. Math.,

(3) (1998), 227-238.

[ 19 ] Jungck, G. and Rhoades, B.E., “Fixed point theorem for occasionally weakly compatible mappings”, Fixed Point

Theory, 7(2006)280-296.

[ 20 ] Olaleru, J., “Common fixed points of three self–mappings in cone metric spaces “, Applied Mathematics E–Notes,

(2011),41–49.

[ 21 ] Sharma, I.R., Rao, J.M., Kumari, P.S. and Panthi, D., “Convergence Axioms on Dislocated Symmetric Spaces”

Spaces, Abstract and Applied Analysis,2014

[ 22 ] Sessa, S. On a weak commutativity condition in fixed point consideration, Publ. Inset. Math., 32 (1982),149-153.

[ 23 ] Singh, A., Dimri, R.C. and Bhatt, S., “A unique common fixed point theorem for four maps in cone metric spaces”,

Int. J. of Math. Analysis, 4(31)(2010), 1511–1517.