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Some Fixed Point Theorems on Meir Keeler Type under Strict Contractions

by Rajeshri Rana, R. C. Dimri, Anita Tomar
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 17 - Number 3
Year of Publication: 2011
Authors: Rajeshri Rana, R. C. Dimri, Anita Tomar
10.5120/2201-2795

Rajeshri Rana, R. C. Dimri, Anita Tomar . Some Fixed Point Theorems on Meir Keeler Type under Strict Contractions. International Journal of Computer Applications. 17, 3 ( March 2011), 24-30. DOI=10.5120/2201-2795

@article{ 10.5120/2201-2795,
author = { Rajeshri Rana, R. C. Dimri, Anita Tomar },
title = { Some Fixed Point Theorems on Meir Keeler Type under Strict Contractions },
journal = { International Journal of Computer Applications },
issue_date = { March 2011 },
volume = { 17 },
number = { 3 },
month = { March },
year = { 2011 },
issn = { 0975-8887 },
pages = { 24-30 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume17/number3/2201-2795/ },
doi = { 10.5120/2201-2795 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:04:40.107423+05:30
%A Rajeshri Rana
%A R. C. Dimri
%A Anita Tomar
%T Some Fixed Point Theorems on Meir Keeler Type under Strict Contractions
%J International Journal of Computer Applications
%@ 0975-8887
%V 17
%N 3
%P 24-30
%D 2011
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper explores the common fixed point theorems involving two pairs of weakly compatible mappings. Also the property (E.A) is proved under a new contractive condition which is independent of the previous known contractive definitions.

References
  1. M.Aamri and D.El.Moutawkil, Some new common fixed point theorems under strict contractive conditions, J.Math.Anal.Appl., 270(1); 181-188,(2002).
  2. C.D.Bari and C.Vetro, Common fixed point for weakly compatible maps satisfying a general contractive condition, Int.J.Math.Math.Sci. Vol 2008.Art. ID 891375, 8 pages.
  3. H.Bouhadjera, General common fixed point theorems for compatible mappings of type (C), Sarajevo J.Math.Vol.1 (14), (2005), 261-270.
  4. H.Bouhadjera and A.Djoudi, General common fixed point theorem for weakly compatible maps, Gen.Mathematics. Vol.16 no.2 (2008), 95-107.
  5. D.W.Boyd and J.S.Wong, On non linear contractions, Proc.Amer.Math.Soc. 20(1969), 458-464.
  6. A.Carbone, B.E.Rhoades and S.P.Singh, A fixed point theorem for generalized contraction map, Indian J.Pure and Appl. Math.20 (1969), 543-548.
  7. J.Jachymski, Common fixed point theorems for some families of maps, Indian J.Pure and Appl. Math.25 (1994), no.9, 925-937.
  8. K.Jha, R.P.Pant, and S.L.Singh, Common fixed points for compatible mappings on metric spaces, Rad.Math.12 (2003), no.1, 107-114.
  9. K.Jha, R.P.Pant, and S.L.Singh, On existence of common fixed point for compatible mappings, J.Math (ISSN 1016-2526), Vol.37 (2005), 37-48.
  10. G.Jungck, Compatible mappings and common fixed points, Int.J.Math.Math. Sci. 9 (1986), 771-779.
  11. G.Jungck, Common fixed point for noncontinous non selfmaps on nonmetric spaces, Far East.J.Math.Sci. 4(2), (1996), 199-215.
  12. G.Jungck, P.P.Murthy and Y.J.Cho, Compatible mappings of type (A) and Common fixed points, Math,Japonica, 38(2), (1993), 381-390.
  13. G.Jungck, K.B.Moon, S.Park and B.E.Rhoades, On generalizations of Meir Keeler type contractive maps corrections, J.Math.Anal.Appl.180 (1993), 221-222.
  14. G.Jungck and B.E.Rhoades, Fixed point for set valued functions without continuity, Indian J.Pure Appl. Math. 29(3), (1998), 227-238.
  15. A.Meir and E.Keeler, A theorem on contractive maps, J.Math.Anal.Appl, 28 (1969), 326-329.
  16. R.P.Pant, Common fixed point of contractive maps, J.Math.Anal.Appl. 226(1998), 251-258.
  17. R.P.Pant, Discontinuity and fixed points, J.Math.Anal.Appl.240 (1), (1999), 284-289.
  18. R.P.Pant, P.C.Joshi, and V.Gupta, A Meir Keeler type fixed point theorem, Indian J.Pure Appl.Math, 32 (6) (2001), 779-787.
  19. S.Park and B.E.Rhoades, Extensions of fixed point theorem of Meir Keeler, Ark.Math. 19 (1991), 223-238.
  20. H.K.Pathak and M.S.Khan, Compatible mappings of type (B) and common fixed point of Gregus type, Czechoslovak Math.J. 45 9120), (1995), 685-698.
  21. H.K.Pathak, Y.J.Cho, S.M.Khan and B.S.Lee, Compatible mappings of type (P) and its applications to dynamic programming, Lee Mathematiche, 50(1995), Fasc. 1, 15-30.
  22. H.K.Pathak, Y.J.Cho, S.M.Khan and B.S.Madharia, Compatible mappings of type (C) and common fixed point theorem of Gregus type, Demonstratio Math. J. 31, (1998), no. 3, 499-518..
  23. S.Sessa, On weak commutativity conditions of mappings in fixed point considerations, Pub.Inst.Math.32 (1998), 149-153.
  24. S.L.Singh and A.Tomar, Weaker forms of commuting maps and existence of fixed pints, J.Korean.Soc.Math.Edu.Ser.B.PureAppl.Math.Vol.10 (3), (2003), 145- 161.
Index Terms

Computer Science
Information Sciences

Keywords

Common fixed point Compatible and Compatible mappings of type (A (B) (C) and (P) Weakly compatible maps property E.A

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