[KSCI] Korea Science Citation Index Service

WEAK INEQUALITIES WITH CONTROL FUNCTIONS AND FIXED POINT RESULTS

Choudhury, Binayak S. (Department of Mathematics, Bengal Engineering and Science University)

Publication Information

Journal of applied mathematics & informatics / v.28, no.3_4, 2010 , pp. 967-976 More about this Journal

Abstract

In recent times control functions have been used in several problems of metric fixed point theory. Also weak inequalities have been considered in a number of works on fixed points in metric spaces. Here we have incorporated a control function in certain weak inequalities. We have established two fixed point theorems for mapping satisfying such inequalities. Our results are supported by examples.

Keywords

Altering distance function; weak inequalities; fixed point; metric space;

Citations & Related Records

Reference

1	S.V.R. Naidu, Some fixed point theorems in Metric spaces by altering distances, Czechoslovak Mathematical Journal, 53(1) (2003), 205-212. DOI ScienceOn
2	K.P.R. Sastry, G.V.R. Babu, Some fixed point theorems by altering distances between the points, Ind. J. Pure. Appl, Math., 30(6) (1999), 641-647.
3	K.P.R. Sastry, S.V.R.Naidu, G.V.R. Babu, G.A.Naidu, Generalization of common fixed point theorems for weakly commuting map by altering distances, Tamkang Jr. Math., 31(3) (2000), 243-250.
4	Y.Song, Coincidence points for noncommuting f-weakly contractive mappings, Int. J. Comput. Appl. Math., (IJCAM), 2(1) (2007), 51-57.
5	Q. Zhang and Y.Song, Fixed point theory for generalized $\phi$ - weak contractions, Applied Mathematics Letters, 22(1) (2009), 75-78. DOI ScienceOn
6	P.N. Dutta and B.S.Choudhury, A Generalisation of Contraction Principle in Metric Spaces, Fixed Point Theory and Applications, 2008, (2008), Article ID 406368,8 pages.
7	B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Analysis: Theory, Methods and Application, 47(4) (2001), 2683-2693. DOI ScienceOn
8	D.Ilic, V.Rakocevic, Common fixed points for maps on cone metric space, J.Math. Anal. Appl., 341 (2008), 876-882. DOI ScienceOn
9	M.S, Khan, M. Swaleh, S. Sessa, Fixed points theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), 1-9. DOI
10	J. Merryfield, B. Rothschild, J. D. Stein, Jr., An application of Ramsey's theorem to the Banach contraction principle, Proceedings of the American Mathematical Society, 130 (4) (2002), 927-933. DOI ScienceOn
11	B.S. Choudhury, P.N. Dutta, Common fixed points for fuzzy mappings using generalized altering distances, Soochow J. Math., 31(1) (2005), 71-81.
12	B.S. Choudhury, K.Das, P.N. Dutta, A fixed point result in Menger spaces using a real function, Acta Math. Hungar., 2008, DOI: 10.1007/s10474-008-7242-3.
13	B.S. Choudhury, P.N. Dutta, A.kundu, Fixed point results using altering distance function and $\phi$ - function in metric spaces, IJMA 5-8, (1-12), 2007, 281-287.
14	C. E. Chidume, H. Zegeye, S. J. Aneke, Approximation of fixed points of weakly contractive nonself maps in Banach spaces, J.Math. Anal. Appl., 270(1) (2002), 189-199. DOI ScienceOn
15	B.S.Choudhury, P.N. Dutta, A unified fixed point result in metric spaces involving a two variable function, Filomat, 14 (2000), 43-48.
16	B.S. Choudhury, A common unique fixed point result in metric spaces involving generalized altering distances, Mathematical Communications, 10 (2005), 105-110.
17	Ya.I.Alber,S.Guerre-Delabriere, Principles of weakly contractive maps in Hilbert spaces, in :I. Gohberg,Yu. Lyubich(Eds.), New Results in Operator Theory, in : Advances and Appl., 98, Birkhuser, Basel, 1997,7-22.
18	B.S. Choudhury, K.Das, A new contraction principle in Menger spaces, Acta Mathematica Sinica, 24(8)(2008), 1379-1386. DOI ScienceOn
19	D.W. Boyd, J.S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., 20 (1969), 458-464. DOI ScienceOn
20	I . Beg, M. Abbas, Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition, Fixed Point Theory and Applications, 2006. Article ID 74503, 7 pages.
21	A. D. Arvanitakis, A proof of the generalized Banach contraction conjecture, Proc. Amer. Math. Soc., 131(12) (2003), 3647-3656. DOI ScienceOn
22	G.V.R.Babu, B.Lalitha and M.L.Sandhya, Common fixed point theorems involving two generalized altering distance functions in four variables, Proc. Jangjeon Math. Soc., 10(1)(2007), 83-93.