Research Article

Fixed Points Theorems for Weakly Compatible Maps along with Property (E.A.)

by  S Mudgal
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 96 - Issue 24
Published: June 2014
Authors: S Mudgal
10.5120/16940-6725
PDF

S Mudgal . Fixed Points Theorems for Weakly Compatible Maps along with Property (E.A.). International Journal of Computer Applications. 96, 24 (June 2014), 5-10. DOI=10.5120/16940-6725

                        @article{ 10.5120/16940-6725,
                        author  = { S Mudgal },
                        title   = { Fixed Points Theorems for Weakly Compatible Maps along with Property (E.A.) },
                        journal = { International Journal of Computer Applications },
                        year    = { 2014 },
                        volume  = { 96 },
                        number  = { 24 },
                        pages   = { 5-10 },
                        doi     = { 10.5120/16940-6725 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2014
                        %A S Mudgal
                        %T Fixed Points Theorems for Weakly Compatible Maps along with Property (E.A.)%T 
                        %J International Journal of Computer Applications
                        %V 96
                        %N 24
                        %P 5-10
                        %R 10.5120/16940-6725
                        %I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, we prove common fixed point theorems for a pair of weakly compatible maps under E. A . property. A major benefit of property (E. A. ) is that it ensures convergence of desired sequences without completeness. At the end we rectify the main result of the paper, entitled "Common fixed points for weakly compatible maps, Proc. Indian Acad. Sci. (Math. Sci. ) Vol. 111(2001), No. 2, pp 241-247.

References
  • M. Aamri and D. EI . Moutawakil , Some new common fixed point theorems under strict contractive conditions , J. Math. Anal. Appl. 270(2002), 181-188.
  • S. Banach, Surles operations dans les ensembles abstraits et leur application aux equationsitegrales, Fund. Math. (1922), 3, 133- 181.
  • R. Chugh and S. Kumar, Common fixed points for weakly compatible maps, Proc. Indian Acad. Sci. (Math. Sci. ), Vol. 111, No. 2(2001), 241- 247.
  • R. Chugh and S. Kumar, Common fixed point theorem using minimal commutativity and reciprocal conditions in metric space, Scientiac Mathematiace Japonica, 56 No. 2 (2002), 269-275.
  • G,Jungck, Commuting mappings and fixed point, Amer. Math. Monthly 83 (1976), 261-263.
  • G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci 9(1986), 771-779.
  • G. Jungck and B. E. Rhoades,Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math. , 29(3) (1998), 227-238.
  • G. Jungck, P. P. Murthy, Y. J. Cho, Compatible mappings of type(A) and Common fixed points, Math. Japonica, 38(1993), 381-390.
  • M. Imdad Javid Ali , Jungck's common fixed point theorem and E. A property, Acta Mathematica Sinica, an. , 2008, Vol. 24, No. 1, pp. 87–94.
  • R Kannan, Some Results on fixed points, Bull. Cal. Math. Soc. , 60, (1968) 71-76.
  • H. K . Pathak, Y. J. Cho, S. M. Kang, Remarks on R-Weakly commuting Mappings and common fixed point theorems, Bull. Korean Math. Soc. 34 (1997),No. 2, pp. 247–257.
  • R. P. Pant, Common fixed points of non commuting mappings, J. Math. Anal. Appl. 188(1994), 436-440.
  • R. P. Pant, Common fixed points theorems for contractive maps, J. Math. Anal. Appl. 226(1998), 251-258.
  • W. F. Pfeffer, More on involutions of a circle, Amer. Math. Monthly, 81 (1974), 613-616.
  • S. Sessa, On a weak commutativity conditions of mappings in fixed point consideration, Publ. Inst. Math. Beograd, 32(46) (1982), 146-153.
Index Terms
Computer Science
Information Sciences
No index terms available.
Keywords

E. A. Property Fixed Points Theorems Weakly Compatible Maps

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