Common fixed points under contractive conditions of integral type

Hakima Bouhadjera

doi:10.2478/gm-2020-0004

.blurhash-client-img { display: none !important; }

Common fixed points under contractive conditions of integral type

General Mathematics

Volume 28 (2020): Issue 1 (June 2020)

By: Hakima Bouhadjera

Open Access

|Jul 2020

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

Articles in this issue

DOI: https://doi.org/10.2478/gm-2020-0004 | Journal eISSN: 1584-3289 | Journal ISSN: 1221-5023

Journal RSS Feed

Language: English

Page range: 41 - 57

Submitted on: Oct 10, 2019

Accepted on: May 25, 2020

Published on: Jul 31, 2020

Published by: Lucian Blaga University of Sibiu

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Weakly compatible mappings,

occasionally weakly compatible mappings,

contractive conditions,

integral type,

common fixed point theorems

Related subjects:

Mathematics,

Differential equations and dynamical systems,

Probability and statistics,

Numerical and computational mathematics,

Applied mathematics

© 2020 Hakima Bouhadjera, published by Lucian Blaga University of Sibiu
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 28 (2020): Issue 1 (June 2020)