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Jungck’s common fixed point theorem and E.A property

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We prove that (E.A) property buys the required containment of range of one mapping into the range of other in common fixed point considerations up to a pair of mappings. While proving our results, we utilize the idea of implicit functions due to Popa, keeping in view their unifying power.

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  1. Jungck, G.: Commuting mappings and fixed points. Amer. Math. Monthly, 83, 261–263 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  2. Sessa, S.: On a weak commutativity condition of mappings in fixed point considerations. Publ. Inst. Math., 32(46), 149–153 (1982)

    MathSciNet  Google Scholar 

  3. Jungck, G.: Compatible mappings and common fixed points. Internat. J. Math. Math. Sci., 9(4), 771–779 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  4. Jungck, G., Murthy, P. P., Cho, Y. J.: Compatible mappings of type (A) and common fixed points. Math. Japon., 38, 381–390 (1993)

    MATH  MathSciNet  Google Scholar 

  5. Jungck, G., Pathak, H. K.: Fixed points via ‘Biased maps’. Proc. Amer. Math. Soc., 123(7), 2049–2060 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  6. Murthy, P. P.: Important tools and possible applications of metric fixed point theory. Nonlinear Anal. (TMA), 47, 3479–3490 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Jungck, G.: Common fixed points for noncontinuous nonself maps on nonmetric spaces. Far East J. Math. Sci., 4(2), 199–215 (1996)

    MATH  MathSciNet  Google Scholar 

  8. Kannan, R.: Some results on fixed points. Bull. Calcutta Math. Soc., 60, 71–76 (1968)

    MATH  MathSciNet  Google Scholar 

  9. Pant, R. P.: A common fixed point theorem under a new condition. Indian J. Pure Appl. Math., 30(2), 147–152 (1999)

    MATH  MathSciNet  Google Scholar 

  10. Singh, S. L., Mishra, S. N.: Remarks on Jachymski’s fixed point theorems for compatible maps. Indian J. Pure Appl. Math., 28(5), 611–615 (1997)

    MATH  MathSciNet  Google Scholar 

  11. Rhoades, B. E.: A comparison of various definitions of contractive mappings. Trans. Amer. Math. Soc., 226, 257–290 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  12. Rhoades, B. E.: Contractive definitions revisited. Contemp. Math., 21, 189–205 (1983)

    MATH  MathSciNet  Google Scholar 

  13. Popa, V.: Some fixed point theorems for compatible mappings satisfying an implicit relation. Demonstratio Math., 32(1), 157–163 (1999)

    MATH  MathSciNet  Google Scholar 

  14. Aamri, M., El Moutawakil, D.: Some new common fixed point theorems under strict contractive conditions. J. Math. Anal. Appl., 270, 181–188 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  15. O’Regan, D., Hussain, N.: Generalized I-contractions and pointwise R-subweakly commuting maps. Acta Mathematica Sinica, English Series, 23(8), 1505–1508 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  16. Bryant, V.W.: A remark on fixed point theorem for iterated mappings. Amer. Math. Monthly, 75, 399–400 (1968)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to M. Imdad.

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This research is supported by U.G.C., India under Project No. F.30-246/2004(SR)

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Imdad, M., Ali, J. Jungck’s common fixed point theorem and E.A property. Acta. Math. Sin.-English Ser. 24, 87–94 (2008).

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