Some common fixed point theorems for Ciric type contraction mappings

Main Article Content

Sumit Chandok

Abstract

Some common fixed point theorems for \'{C}iri\'{c} type contraction mappings have been obtained in convex metric spaces. As applications, invariant approximation results for these type of mappings are obtained. The proved results generalize, unify and extend some of the results of the literature.

Article Details

How to Cite
Chandok, S. (2012). Some common fixed point theorems for Ciric type contraction mappings. Tamkang Journal of Mathematics, 43(2), 187–202. https://doi.org/10.5556/j.tkjm.43.2012.770
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Papers

References

M. A. Al-Thagafi, Common fixed points and best approximation, J. Approx. Theory 85(1996), 318-323.

M. A. Al-Thagafi and N. Shahzad, Noncommuting self maps and invariant approximations, Nonlinear Analysis 64(2006), No. 12, 2778-2786.

G. V. R. Babu and K. N. V. V. Vara Prasad, Common fixed point theorems of different compatible type mappings using Ciric's contraction type condition, Math. Comm. 11(2006), 87-102.

S. Chandok and T. D. Narang, Common fixed points and invariant approximation for Gregus type contraction mappings, Rendiconti Circolo Mat. Palermo, 60(2011), 203-214.

L. Ciric, On a common fixed point theorem of a Gregus type, Publ. Inst. Math. 49(1991), 174-178.

L. Ciric, On Diviccaro, Fisher and Sessa open questions, Arch. Math. (BRNO) 29(1993), 145-152.

M. L. Diviccaro, B. Fisher, S. Sessa, A common fixed point theorem of Gregus type, Publ. Math. Debrecen 34(1987), 83-89.

B. Fisher and S. Sessa, On a fixed point theorem of Gregus, Internat. J. Math. Math. 9(1986), 23-28.

M. D. Guay, K. L. Singh and J. H. M. Whitfield, Fixed point theorems for nonexpansive mappings in convex metric spaces, Proc. Conference on nonlinear analysis (Ed. S.P.Singh and J. H. Bury) Marcel Dekker 80(1982), 179-189.

M. Gregus, A fixed point theorem in Banach space, Boll. Un. Mat. Ital. (5) 7-A (1980), 193-198.

M. Grinc and L. Snoha, textit{Jungck theorem for triangular maps and related results, Appl. General Topology 1(2000), 83-92.

L. Habiniak, Fixed point theorems and invariant approximation, J. Approx. Theory 56(1989), 241-244.

N. Hussain, B. E. Rhoades and G. Jungck, Common fixed point snf invariant approximation results for Gregus type I-contractions, Num. Func. Anal. Optim. 28(2007), 1139-1151.

G. Jungck, On a fixed point theorem of Fisher and Sessa, Internat. J. Math. Math. Sci. 13(1990), 497-500.

G. Jungck, Common fixed point theorems for compatible self maps of Hausdorff topological spaces, Fixed Point Theory Appl.3(2005), 355-363.

G. Jungck and S. Sessa, Fixed point theorems in best approximation theory, Math. Japon. 42(1995), 249-252.

R. N. Mukherjee and V. Verma, A note on a fixed point theorem of Gregus, Math. Japon. 33(1988), 745-749.

T. D. Narang and S. Chandok, Fixed points of quasi-nonexpansive mappings and best approximation, Selcuk J. Appl. Math. 10(2009), 75-80.

T. D. Narang and S. Chandok, Fixed points and best approximation in metric spaces}, Indian J. Math. 51(2009), 293-303.

T.D. Narang and S. Chandok, Common fixed points and invariant approximation of $R$-subweakly commuting maps in convex metric spaces, Ukrainian Math. J. 62(2010), 1367-1376.

S. A. Sahab, M. S. Khan and S. Sessa, A result in best approximation theory, J. Approx. Theory 55(1988), 349-351.

N. Shahzad, Invariant approximations and $R$-subweakly commuting maps, J. Math. Anal. Appl. 257 (2001), 39-45.

N. Shahzad, Noncommuting maps and best approximations, Rad. Math. 10(2001), 77-83.

S. P. Singh, An application of fixed point theorem to approximation theory, J. Approx. Theory 25(1979), 89-90.

A. Smoluk, Invariant approximations, Mat. Stos. 17(1981), 17-22.

P.V. Subrahmanyam, An application of a fixed point theorem to best approximation, J. Approx. Theory 20(1977), 165-172.

W. Takahashi, A convexity in metric space and nonexpansive mappings I, Kodai Math. Sem. Rep. 22(1970), 142-149.