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Keywords:
common fixed point; metric space; b-metric space; property (E.A); implicit relation; expansive mapping
common fixed point; metric space; b-metric space; property (E.A); implicit relation; expansive mapping
Summary:
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.
References:
[1] Aamri, M., El Moutawakil, D.: Some new common fixed point theorems under strict contractive conditions. Math. Anal. Appl. 270 (2002), 181–188. DOI 10.1016/S0022-247X(02)00059-8 | MR 1911759 | Zbl 1008.54030
[2] Czerwik, S.: Contraction mappings in b-metric spaces. Acta Math. Inform. Univ. Ostraviensis 1 (1993), 5–11. MR 1250922 | Zbl 0849.54036
[3] Czerwik, S.: Nonlinear set-valued contraction mappings in b-metric spaces. Atti Sem. Mat. Fis. Univ. Modena 46, 2 (1998), 263–276. MR 1665883 | Zbl 0920.47050
[4] Djoudi, A.: General fixed point theorems for weakly compatible maps. Demonstratio Math. 38 (2005), 195–205. MR 2123734 | Zbl 1065.54020
[5] Imdad, M., Khan, T. I.: Fixed point theorems for some expansive mapping via implicit relations. Nonlinear Analysis Forum 9, 2 (2004), 209–218. MR 2112009
[6] Imdad, M., Ali, J.: Jungck’s Common Fixed Point Theorem and E.A Property. Acta Mathematica Sinica, English Series 24, 1 (2008), 87–94. DOI 10.1007/s10114-007-0990-0 | MR 2384234 | Zbl 1158.54021
[7] Jungck, G.: Compatible mappings and common fixed points. Internat. J. Math. Math. Sci. 9 (1986), 771–779. DOI 10.1155/S0161171286000935 | MR 0870534
[8] Jungck, G.: Common fixed points for noncontinuous nonself mappings on nonnumeric spaces. Far. East, J. Math.Sci. 4 (1996), 199–215. MR 1426938
[9] Pant, R. P.: Common fixed points of contractive maps. J. Math. Anal. Appl. 226 (1998), 251–258. DOI 10.1006/jmaa.1998.6029 | MR 1646430
[10] Pant, R. P.: R-weak commutativity and common fixed points of noncompatible maps. Ganita 49, 1 (1998), 19–27. MR 1655883 | Zbl 0977.54039
[11] Pant, R. P.: R-weak commutativity and common fixed points. Soochow J. Math. 25 (1999), 37–42. MR 1681606 | Zbl 0918.54038
[12] Popa, V.: Fixed point theorems for implicit contractive mappings. Stud. Cerc. St. Ser. Mat. Univ. Bacău 7 (1997), 127–133. MR 1721711 | Zbl 0967.54041
[13] Popa, V.: Some fixed point theorems for compatible mappings satisfying an implicit relation. Demonstratio Math. 32 (1999), 157–163. MR 1691726 | Zbl 0926.54030
[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. MR 2478955 | Zbl 1199.54242
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