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Reseach Article

Fixed Point Theorems for the Maps Satisfying Contractive Condition of Integral Type in Metric Spaces

by Avinash Chandra Upadhyaya
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 159 - Number 1
Year of Publication: 2017
Authors: Avinash Chandra Upadhyaya
10.5120/ijca2017912511

Avinash Chandra Upadhyaya . Fixed Point Theorems for the Maps Satisfying Contractive Condition of Integral Type in Metric Spaces. International Journal of Computer Applications. 159, 1 ( Feb 2017), 12-15. DOI=10.5120/ijca2017912511

@article{ 10.5120/ijca2017912511,
author = { Avinash Chandra Upadhyaya },
title = { Fixed Point Theorems for the Maps Satisfying Contractive Condition of Integral Type in Metric Spaces },
journal = { International Journal of Computer Applications },
issue_date = { Feb 2017 },
volume = { 159 },
number = { 1 },
month = { Feb },
year = { 2017 },
issn = { 0975-8887 },
pages = { 12-15 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume159/number1/26965-2017912511/ },
doi = { 10.5120/ijca2017912511 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-07T00:04:33.849384+05:30
%A Avinash Chandra Upadhyaya
%T Fixed Point Theorems for the Maps Satisfying Contractive Condition of Integral Type in Metric Spaces
%J International Journal of Computer Applications
%@ 0975-8887
%V 159
%N 1
%P 12-15
%D 2017
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, we prove fixed point theorems for the maps satisfying contractive condition of integral type using occasionally weakly compatible maps along with property (E.A.).

References
  1. M. Aamri and D. El. Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 27(2002),181-188.
  2. M. A. Al-Thagafi, N. Shahzad, Generalized I-nonexpansive selfmaps and invariant approximations, Acta Math. Sin.(Engl. Ser.) 24(2008) 867-876.
  3. M. A. Al-Thagafi, N. Shahzad, A note on occasionally weakly compatible maps, Int. J. Math. Anal., 3(2) (2009) 55-58.
  4. I. Altun, D. Turkoglu, B. E. Rhoades, Fixed points of weakly compatible maps satisfying a general contractive condition of integral type, Fixed Point Theory Appl. 2007 (2007) Article ID 17301, 9 pages.
  5. G. V. R. Babu, G. N. Alenmayehu, A common fixed point theorem for weakly contractive mappings satisfying property (E.A.), Appl. Math. E-Notes 10 (2010) 167-174.
  6. G. V. R. Babu, G. N. Alenmayehu, Points of coincidence and common fixed points of a pair of generalized weakly contractive mappings, J. Adv. Res. Pure Math., 2(2) (2010) 89-106.
  7. G. V. R. Babu, G. N. Alenmayehu, Common fixed point theorems for occasionally weakly compatible maps satisfying property (E.A.) using an inequality involving quadratics terms, Applied Mathematics Letters 24(2011) 975-981.
  8. A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29 (2002) 531-536.
  9. A. Djoudi, A Aliouche, Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl., 329 (2007) 31-45.
  10. G. Jungck, Common fixed points for non-continuous non-self maps on non-metric spaces, Far East J. Math. Sci., 4(2) (1996), 199-215.
  11. G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9(4) (1986), 771-779.
  12. G. Jungck, Commuting mappings and fixed points. Amer. Math. Monthly,83, (1976), 261-263.
  13. G. Jungck, B. E. Rhoades, Fixed points for set-valued functions without continuity, Indian J. Pure Appl. Math., 29(3) (1998) 227-238.
  14. G. Jungck, B. E. Rhoades, Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory 7(2006) 286-296.
  15. R. Kannan, Some results on fixed points, Bull. Cal. Math. Soc., 60 (1968), 71-76.
  16. W. Liu, J. Wu, Z. Li, Common fixed points of single-valued and multi-valued maps, Int. J. Math. Math. Sci. 19 (2005) 3045-3055.
  17. A. Meir, E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl., 28 (1969) 326-329.
  18. H. K. Pathak, Rosana Rodriguez-Lopez and R. K. Verma,A common fixed point theorem using implicit relation and property (E.A.) in metric spaces, Filomat 21(2) (2007), 211–234.
  19. B. E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 63 (2003) 4007-4013.
  20. S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math., 32 (1982) 149-153.
  21. T. Suzuki, Meir-Keeler contractions of integral type are still Meir-Keeler contractions, Int. J. Math. Math. Sci., 2007 (2007) Article ID 39281, 6 pages.
  22. C. Vetro, On Branciari’s theorem for weakly compatible mappings, Applied Mathematics Letters 23 (2010) 700-705.
  23. P. Vijayaraju, B. E. Rhoades, R. Mohanraj, A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 15 (2005) 2359-2364.
Index Terms

Computer Science
Information Sciences

Keywords

Weakly compatible maps occasionally weakly compatible maps property (E.A. ) and Common property (E.A.). Subject classification: (2001) AMS 47 H10 54 H25.