Geodesic
A Common Fixed Point Theorem for Expansive Mappings under Strict Implicit Conditions on b-Metric Spaces
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 1, pp. 5-15 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 47H10, 54H25
Keywords: common fixed point; metric space; b-metric space; property (E.A); implicit relation; expansive mapping 
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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, Tome 50 (2011) no. 1, pp. 5-15. http://geodesic.mathdoc.fr/item/AUPO_2011_50_1_a0/

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