A NOTE ON SOME FIXED POINT THEOREMS ON G-METRIC SPACES

Jing Chen; Chuanxi Zhu; Li Zhu

doi:10.11948/20190125

2021 Volume 11 Issue 1

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Jing Chen, Chuanxi Zhu, Li Zhu. A NOTE ON SOME FIXED POINT THEOREMS ON G-METRIC SPACES[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 101-112. doi: 10.11948/20190125

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Jing Chen, Chuanxi Zhu, Li Zhu. A NOTE ON SOME FIXED POINT THEOREMS ON G-METRIC SPACES[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 101-112. doi: 10.11948/20190125

A NOTE ON SOME FIXED POINT THEOREMS ON G-METRIC SPACES

1.
Department of Mathematics, Nanchang University, 330031 Nanchang, China
2.
Department of Mathematics, Jiangxi Agricultural University, 330045 Nanchang, China

Corresponding author: Email address:chuanxizhu@126.com(C. Zhu)
Fund Project: The authors were supported by National Natural Science Foundation of China(11771198) and Science and Technology Program of Department of Education of Jiangxi Province (GJJ190183, GJJ160380)

Abstract

Abstract

In this paper, we prove some fixed point theorems in the framework of G-metric spaces that cannot be obtained from the existence results in the context of quasi-metric spaces.
- G-metric /
- quasi-metric /
- fixed point
MSC: 47H10, 54H25, 54D99, 54E99

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References

[1]	T. V. An, N. V. Dung and V. T. L. Hang, A new approach to fxed point theorems on G-metric spaces, Topology Appl., 2013, 160, 1486–1493. doi: 10.1016/j.topol.2013.05.027 CrossRef Google Scholar
[2]	M. Asadi, E. Karapınar and P. Salimi, A new approach to G-metric and related fxed point theorems, J. Inequal. Appl., 2013. DOI: 10.1186/1029–242X–2013–454. CrossRef Google Scholar
[3]	R. P. Agarwal, E. Karapınar and A. F. R. L. Hierro, Last remarks on G-metric spaces and related fxed point theorems, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 2016, 110, 433–456. doi: 10.1007/s13398-015-0242-6 CrossRef Google Scholar
[4]	H. Aydi, A. Felhi and S. Sahmim, Related fxed point results for cyclic contractions on G-metric spaces and application, Filomat, 2017, 31(3), 853–869. doi: 10.2298/FIL1703853A CrossRef Google Scholar
[5]	H. Aydi, M. Postolache and W. Shatanawi, Coupled fxed point results for (ψ, ϕ)-weakly contractive mappings in ordered G-metric spaces, Comput. Math. Appl., 2012, 63(1), 298–309. doi: 10.1016/j.camwa.2011.11.022 CrossRef Google Scholar
[6]	M. Abbas, A. Hussain, B. Popovic and S. Radenovic, Istratescu-Suzuki-Cirictype fxed points results in the framework of G-metric spaces, J. Nonlinear Sci. Appl., 2016, 9(12), 6077–6095. doi: 10.22436/jnsa.009.12.15 CrossRef Google Scholar
[7]	S. Cobzaş, Functional analysis in Asymmetric Normed Spaces, Birkhäuser, Springer, Basel, 2013. Google Scholar
[8]	H. Ding and E. Karapınar, A note on some couple fxed-point theorems on G-metric spaces, J. Inequal. Appl., 2012. DOI: 10.1186/1029–242X–2012–170. CrossRef Google Scholar
[9]	Y. U. Gaba, Fixed point theorems in G-metric spaces, J. Math. Anal. Appl., 2017, 455, 528–537. doi: 10.1016/j.jmaa.2017.05.062 CrossRef Google Scholar
[10]	M. Jleli and B. Samet, Rmarks on G-metric spaces and fxed poit theorems, Fixed Point Theory Appl., 2012. DOI: 10.1186/1687–1812–2012–210. CrossRef Google Scholar
[11]	E. Karapınar and R. P. Agarwal, Further fxed point results on G-metric spaces, Fixed Point Theory Appl., 2013. DOI: 10.1186/1687–1812–2013–154. CrossRef Google Scholar
[12]	A. Latif and T. Nazir, Common fxed point of generalized contraction type mappings in ordered G-metric spaces, J. Nonlinear Convex Anal., 2018, 19(7), 1275–1285. Google Scholar
[13]	Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 2006, 7, 289–297. Google Scholar
[14]	Z. Mustafa, H. Obiedat and F. Awawdeh, Some fxed point theorem for mapping on complete G-metric sapces, Fixed Point Theory Appl., 2008. DOI: 10.1155/2008/189870. CrossRef Google Scholar
[15]	Z. Mustafa, M. Khandagji and W. Shatanawi, Fixed point results on complete G-metric spaces, Stud. Sci. Math. Hung., 2011, 48(3), 304–319. Google Scholar
[16]	Z. Mustafa, M. Arshad, S. U. Khan, J. Ahmad and M. M. M. Jaradat, Common fxed points for multivalued mappings in G-metric spaces with applications, J. Nonlinear Sci. Appl., 2017, 10, 2550–2564. doi: 10.22436/jnsa.010.05.23 CrossRef Google Scholar
[17]	Z. Mustafa, H. Aydi and E. Karapınar, On common fxed points in G-metric spaces using (E.A) property, Comput. Math. Appl., 2012, 64(6), 1944–1956. doi: 10.1016/j.camwa.2012.03.051 CrossRef Google Scholar
[18]	I. L. Reilly, P. V. Subrahmanyam and M. K. Vamanamurthy, Cauchy sequences in quasi-pseudo-metric spaces, Monatsh. Math., 1982, 93, 127–140. doi: 10.1007/BF01301400 CrossRef Google Scholar
[19]	A. F. Roldán López de Hierro, E. Karapınar and D. O'Regan, Coincidence point theorems on quasi-metric spaces via simulation functions and applications to G-metric spaces, J. Fixed Point Theory Appl., 2018. DOI: 10.1007/s11784– 018–0582–x. CrossRef Google Scholar
[20]	B. Samet, C. Vetro, F. Vetro and S. Nicaise, Rmarks on G-metric spaces, Int. J. Anal., 2013. DOI: 10.1155/2013/917158. CrossRef Google Scholar
[21]	W. Shatanawi, Fixed point theory for contractive mappings satisfying ϕ-Maps in G-metric Spaces, Fixed Point Theory Appl., 2010. DOI: 10.1155/2010/181650. CrossRef Google Scholar
[22]	W. A. Wilson, On quasi-metric spaces, Am. J. Math., 1931, 53, 675–684. doi: 10.2307/2371174 CrossRef Google Scholar
[23]	L. Zhu, C. Zhu and C. Chen, Commen fxed point theorems for fuzzy mappings in G-metric spaces, Fixed Point Theory Appl., 2012. DOI: 10.1186/1687–1812– 2012–159. CrossRef Google Scholar
[24]	A. Zada, R. Shah and T. Li, Integral type contraction and coupled coincidence fxed point theorems for two pairs in G-metric spaces, Hacet. J. Math. Stat., 2016, 45(5), 1475–1484. Google Scholar
[25]	D. Zheng, Fixed point theorems for generalized θ - ϕ-contractions in G-metric spaces, J. Funct. Spaces, 2018. DOI: 10.1155/2018/1418725. CrossRef Google Scholar