Common fixed points under contractive conditions of integral type

Bouhadjera, Hakima

doi:10.2478/gm-2020-0004

Abstract

In this paper, we give some common fixed point theorems for a class of occasionally weakly compatible mappings satisfying contractive conditions of integral type. Our results generalize a host of previously theorems. We also present some illustrative examples which support our main results and show the applicability and validity of these results.

References

[1] M. A. Al-Thagafi, N. Shahzad, Generalized I-nonexpansive selfmaps and invariant approximations, Acta Math. Sin. (Engl. Ser.), vol. 24, no. 5, 2008, 867–876.10.1007/s10114-007-5598-x
Search in Google Scholar Back to article
[2] H. Bouhadjera, General common fixed point theorems for compatible mappings of type (C), Sarajevo J. Math., vol. 14, no. 2, 2005, 261–270.
Search in Google Scholar Back to article
[3] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., vol. 29, no. 9, 2002, 531–536.10.1155/S0161171202007524
Search in Google Scholar Back to article
[4] G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., vol. 9, no. 4, 1986, 771–779.10.1155/S0161171286000935
Search in Google Scholar Back to article
[5] G. Jungck, Common fixed points for noncontinuous nonself maps on non-metric spaces, Far East J. Math. Sci., vol. 4, no. 2, 1996, 199–215.
Search in Google Scholar Back to article
[6] G. Jungck, P. P. Murthy, Y. J. Cho, Compatible mappings of type (A) and common fixed points, Math. Japon., vol. 38, no. 2, 1993, 381–390.
Search in Google Scholar Back to article
[7] G. Jungck, B. E. Rhoades, Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory, vol. 7, no. 2, 2006, 287–296.
Search in Google Scholar Back to article
[8] J. K. Kohli, S. Vashistha, Common fixed point theorems for compatible and weakly compatible mappings satisfying general contractive type conditions, Stud. Cercet. Ştiinţ. Ser. Mat. Univ. Bacău, vol. 16, 2006, 33–41.
Search in Google Scholar Back to article
[9] S. Kumar, R. Chugh, R. Kumar, Fixed point theorem for compatible mappings satisfying a contractive condition of integral type, Soochow J. Math., vol. 33, no. 2, 2007, 181–185.
Search in Google Scholar Back to article
[10] H. K. Pathak, Y. J. Cho, S. M. Kang, B. S. Lee, Fixed point theorems for compatible mappings of type (P) and applications to dynamic programming, Matematiche (Catania), vol. 50, no. 1, 1995, 15–33.
Search in Google Scholar Back to article
[11] H. K. Pathak, Y. J. Cho, S. M. Kang, B. Madharia, Compatible mappings of type (C) and common fixed point theorems of Greguš type, Demonstratio Math., vol. 31, no. 3, 1998, 499–518.
Search in Google Scholar Back to article
[12] H. K. Pathak, M. S. Khan, Compatible mappings of type (B) and common fixed point theorems of Greguš type, Czechoslovak Math. J., vol. 45, no. 4, 1995, 685–698.10.21136/CMJ.1995.128555
Search in Google Scholar Back to article
[13] H. K. Pathak, R. Tiwari, M. S. Khan, A common fixed point theorem satisfying integral type implicit relations, Appl. Math. E-Notes, vol. 7, 2007, 222–228.
Search in Google Scholar Back to article
[14] V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math., vol. 32, no. 1, 1999, 157–163.10.1515/dema-1999-0117
Search in Google Scholar Back to article
[15] V. Popa, Common fixed point theorems for compatible mappings of type (A) satisfying an implicit relation, Stud. Cercet. Ştiinţ. Ser. Mat. Univ. Bacău, vol. 9, 1999, 165–172.10.1515/dema-1999-0117
Search in Google Scholar Back to article
[16] V. Popa, A general fixed point theorem for compatible mappings of type (P), Stud. Cercet. Ştiinţ. Ser. Mat. Univ. Bacău, vol. 11, 2001, 153–157.
Search in Google Scholar Back to article
[17] V. Popa, A general fixed point theorem for four weakly compatible mappings satisfying an implicit relation, Filomat, vol. 19, 2005, 45–51.10.2298/FIL0519045P
Search in Google Scholar Back to article
[18] B. E. Rhoades, Two fixed-point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., vol. 63, 2003, 4007–4013.10.1155/S0161171203208024
Search in Google Scholar Back to article
[19] S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math., vol. 32, no. 46, 1982, 149–153.
Search in Google Scholar Back to article

Common fixed points under contractive conditions of integral type

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