A Common Fixed Point Theorem for Expansive Mappings under Strict Implicit Conditions on b-Metric Spaces

Mohamed Akkouchi

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2011)

  • Volume: 50, Issue: 1, page 5-15
  • ISSN: 0231-9721

Abstract

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In the setting of a b-metric space (see [Czerwik, S.: Contraction mappings in b-metric spaces Acta Math. Inform. Univ. Ostraviensis 1 (1993), 5–11.] and [Czerwik, S.: Nonlinear set-valued contraction mappings in b-metric spaces Atti Sem. Mat. Fis. Univ. Modena 46, 2 (1998), 263–276.]), we establish two general common fixed point theorems for two mappings satisfying the (E.A) condition (see [Aamri, M., El Moutawakil, D.: Some new common fixed point theorems under strict contractive conditions Math. Anal. Appl. 270 (2002), 181–188.]) under strict expansive conditions using two classes of implicit relations. These two theorems may be considered as extensions of the main result of [Popa, V.: A General fixed point theorem for expansive mappings under strict implicit conditions Stud. Cerc. St. Ser. Mat. Univ. Bacău 17 (2007), 197–200.] to b-metric spaces. Also, the main result of [Aamri, M., El Moutawakil, D.: Some new common fixed point theorems under strict contractive conditions Math. Anal. Appl. 270 (2002), 181–188.] is obtained as a consequence of our results.

How to cite

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Akkouchi, Mohamed. "A Common Fixed Point Theorem for Expansive Mappings under Strict Implicit Conditions on b-Metric Spaces." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 50.1 (2011): 5-15. <http://eudml.org/doc/196595>.

@article{Akkouchi2011,
abstract = {In the setting of a b-metric space (see [Czerwik, S.: Contraction mappings in b-metric spaces Acta Math. Inform. Univ. Ostraviensis 1 (1993), 5–11.] and [Czerwik, S.: Nonlinear set-valued contraction mappings in b-metric spaces Atti Sem. Mat. Fis. Univ. Modena 46, 2 (1998), 263–276.]), we establish two general common fixed point theorems for two mappings satisfying the (E.A) condition (see [Aamri, M., El Moutawakil, D.: Some new common fixed point theorems under strict contractive conditions Math. Anal. Appl. 270 (2002), 181–188.]) under strict expansive conditions using two classes of implicit relations. These two theorems may be considered as extensions of the main result of [Popa, V.: A General fixed point theorem for expansive mappings under strict implicit conditions Stud. Cerc. St. Ser. Mat. Univ. Bacău 17 (2007), 197–200.] to b-metric spaces. Also, the main result of [Aamri, M., El Moutawakil, D.: Some new common fixed point theorems under strict contractive conditions Math. Anal. Appl. 270 (2002), 181–188.] is obtained as a consequence of our results.},
author = {Akkouchi, Mohamed},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {common fixed point; metric space; b-metric space; property (E.A); implicit relation; expansive mapping; common fixed point; -metric space; property (E.A); implicit relation; expansive mapping},
language = {eng},
number = {1},
pages = {5-15},
publisher = {Palacký University Olomouc},
title = {A Common Fixed Point Theorem for Expansive Mappings under Strict Implicit Conditions on b-Metric Spaces},
url = {http://eudml.org/doc/196595},
volume = {50},
year = {2011},
}

TY - JOUR
AU - Akkouchi, Mohamed
TI - A Common Fixed Point Theorem for Expansive Mappings under Strict Implicit Conditions on b-Metric Spaces
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2011
PB - Palacký University Olomouc
VL - 50
IS - 1
SP - 5
EP - 15
AB - In the setting of a b-metric space (see [Czerwik, S.: Contraction mappings in b-metric spaces Acta Math. Inform. Univ. Ostraviensis 1 (1993), 5–11.] and [Czerwik, S.: Nonlinear set-valued contraction mappings in b-metric spaces Atti Sem. Mat. Fis. Univ. Modena 46, 2 (1998), 263–276.]), we establish two general common fixed point theorems for two mappings satisfying the (E.A) condition (see [Aamri, M., El Moutawakil, D.: Some new common fixed point theorems under strict contractive conditions Math. Anal. Appl. 270 (2002), 181–188.]) under strict expansive conditions using two classes of implicit relations. These two theorems may be considered as extensions of the main result of [Popa, V.: A General fixed point theorem for expansive mappings under strict implicit conditions Stud. Cerc. St. Ser. Mat. Univ. Bacău 17 (2007), 197–200.] to b-metric spaces. Also, the main result of [Aamri, M., El Moutawakil, D.: Some new common fixed point theorems under strict contractive conditions Math. Anal. Appl. 270 (2002), 181–188.] is obtained as a consequence of our results.
LA - eng
KW - common fixed point; metric space; b-metric space; property (E.A); implicit relation; expansive mapping; common fixed point; -metric space; property (E.A); implicit relation; expansive mapping
UR - http://eudml.org/doc/196595
ER -

References

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  2. Czerwik, S., Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis 1 (1993), 5–11. (1993) Zbl0849.54036MR1250922
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  9. Pant, R. P., 10.1006/jmaa.1998.6029, J. Math. Anal. Appl. 226 (1998), 251–258. (1998) MR1646430DOI10.1006/jmaa.1998.6029
  10. Pant, R. P., R-weak commutativity and common fixed points of noncompatible maps, Ganita 49, 1 (1998), 19–27. (1998) Zbl0977.54039MR1655883
  11. Pant, R. P., R-weak commutativity and common fixed points, Soochow J. Math. 25 (1999), 37–42. (1999) Zbl0918.54038MR1681606
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  14. Popa, V., A General fixed point theorem for expansive mappings under strict implicit conditions, Stud. Cerc. St. Ser. Mat. Univ. Bacău 17 (2007), 197–200. (2007) Zbl1199.54242MR2478955

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