Kannan Type Mapping in Tvs-Valued Cone Metric Spaces and Their Application to Urysohn Integral Equations
DOI:
https://doi.org/10.5644/SJM.09.2.09Keywords:
Kannan mapping, fixed point, TVS-valued cone metric space, Urysohn integral equationAbstract
We obtain sufficient conditions for the existence of a common fixed point of three mappings satisfying Kannan type conditions in TVS valued cone metric spaces. We also give an application by finding the solution for a system of two Urysohn integral equations. Our results generalize several well-known recent results in the literature.
2010 Mathematics Subject Classification. 47H10, 47H09, 45N05, 46N20 54H25.
Downloads
References
M. Abbas and G. Jungck, Common fixed point results for non commuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), 416-420.
M. Arshad, A. Azam and P. Vetro, Some common fixed point results in cone metric spaces, Fixed Point Theory Appl., 2009 (2009), Article ID 493965, 11 pages.
A. Azam, I. Beg and M. Arshad, Fixed point in topological vector space valued cone metric spaces, Fixed Point Theory Appl., 2010 (2010), Article ID 604084, 9 pages.
S. Banach, Sur les op´erations dans les ensembles abstraits et leur application aux ´equations int´egrales, Fundam. Mat., 3 (1922), 133–181.
I. Beg, A. Azam and M. Arshad, Common fixed points for maps on topological vector space valued cone metric spaces, Int. J. Math. Math. Sci., 2009 (2009), Article ID. 560264, 8 pages.
S.K. Chatterjea, Fixed-point theorems, C.R. Acad. Bulgare Sci., 25 (1972), 727-730.
E. H. Connell, Properties of fixed point spaces, Proc. Amer. Math. Soc., 10 (6) (1959), 974–979.
M. Djordjevi´c, D. Djori´c, Z. Kadelburg, S. Radenovi´c and D. Spasi´c, Fixed point results under c-distance in tvs-cone metric spaces, Fixed Point Theory Appl., 2011:29, doi: 10.1186/1687-1812-2011-29 (2011).
L.-G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468–1476.
S. Jankovi´c, Z. Kadelburg and S. Radenovi´c, On cone metric spaces: a survey, Nonlinear Anal., 74 (2011), 2591-2601.
Z. Kadelburg, S. Radenovi´c, V. Rakoˇcevi´c, Topological vector spaces valued cone metric spaces and fixed point theorems, Fixed Point Theory Appl., 2010, Article ID 170253, (2010), 18 pages.
Z. Kadelburg and S. Radenovi´c, Coupled fixed point results under TVS-cone metric and W-cone-distance, Adv. Fixed Point Theory, 2 (1)(2012), 29-46.
R. Kannan, Some results on fixed points II, Am. Math. Mon., 76 (4) (1969), 405–408.
D. Ili´c and V. Rakoˇcevi´c, Common fixed points for maps on cone metric space, J. Math. Anal. Appl., 341 (2008), 876–882.
S. Rezapour and R. Hamlbarani, Some notes on paper “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 345 (2008) 719–724.
S. Radenovi´c, Common fixed points under contractive conditions in cone metric spaces, Comput. Math Appl., (2009) doi:10.1016/j.camwa.2009.07.035.
S. Radenovi´c and B.E. Rhoades, Fixed point theorem for two non-self mappings in cone metric spaces, Comput. Math. Appl.,57 (2009) 1701–1707.
P. V. Subrahmanyam, Completeness and fixed-points, Monatsh. Math., 80 (4) (1975), 325–330.
D. Wei-Shih, A note on cone metric fxed point theory and its equivalence, Nonlinear Anal., 72 (2010), 2259-2261.
