Some extensions of banach contraction principle in G-metric spaces

• Autorzy: Gaba Y. U.

Identyfikatory

DOI

10.1515/fascmath-2018-0017

• Języki publikacji: EN

Abstrakty

EN

We present different extensions of the Banach contraction principle in the G-metric space setting. More precisely, we consider mappings for which the contractive condition is satisfied by a power of the mapping and for which the power depends on the specified point in the space. We first state the result in the continuous case and later, show that the continuity is indeed not necessary. Imitating some techniques obtained in the metric case, we prove that under certain conditions, it is enough for the contractive condition to be verified on a proper subset of the space under consideration. These results generalize well known comparable results.

Słowa kluczowe

EN

G-metrics; fixed point; contraction

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2018
• Tom: Nr 61
• Strony: 55--70
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Gaba Y. U.

• Institut de Mathématiques et de Sciences Physiques (IMSP) 01 BP 613 Porto-Novo, Bénin and African Center for Advanced Studies (ACAS) P.O. Box 4477, Yaounde, Cameroon

Bibliografia

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• [2] Aydi H., Shatanawi W., Vetro C., On generalized weakly G-contraction mapping in G-metric spaces, Comput. Math. Appl., 62(2011), 4222-4229.
• [3] Aydi A., Damjanovic B., Samet B., Shatanawi W., Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces, Mathematical and Computer Modelling, 54(2011) 2443-2450.
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• [6] Gaba Y.U., Fixed points of rational type contractions in G-metric spaces, Cogent Mathematics & Statistics, 5(1)(2018).
• [7] Gaba Y.U., Common fixed points in G-metric type spaces via ⅄-sequences, Journal of Mathematics, Volume 2017, Article ID 6018054, 7 pages.
• [8] Gaba Y.U., Fixed point theorems in G-metric spaces, Journal of Mathematical Analysis and Applications, 455(1)(2017), 528-537.
• [9] Gajić L.J., Lozanov-Crvenković Z., A fixed point result for mappings with contractive iterate at a point in G-metric spaces, Filomat, 25(2)(2011), 53-58.
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• [11] Mustafa Z., A new structure for generalized metric spaces with applications to fixed point theory, Ph.D. thesis, The University of Newcastle, Australia (2005).
• [12] Mustafa Z., Aydi H., Karapinar E., Mixed g-monotone property and quadruple fixed point theorems in partially ordered metric spaces, Fixed Point Theory and Applications, 2012, 71(2012).
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• [14] Rhoades B.E., A comparison of various definitions of contractive mappings, Proc. Am. Math. Soc., 226(1977), 257-290.
• [15] Shirali S., Maps for which some power is a contraction, Math. Communi., 15(1)(2010), 139-141.
• [16] Tahat N., Aydi H., Karapinar E., Shatanawi W., Common fixed points for single-valued and multi-valued maps satisfying a generalized contraction in G-metric spaces, Fixed Point Theory Appl. 2012, 48(2012).

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).