Picard sequence in complete Gb-metric spaces and fixed points results
Abstract
Our idea in this article to introduce Picard sequence in complete Gb-metric spaces and explain some useful outcomes in the structure of Gb-metric spaces. We are extending the conclusions of Khojasteh et al. [6] and Isa Yildirim and Arslan Hojat Ansari [16]. An example and some corollaries are also proved to show the usefulness of our results.
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References
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2. Aydi H. , Abbas M. , Sintunavarat W., and Kumam P., “Tripled fixed point of W-compatible mappings in abstract metric spaces”, Fixed Point Theory and Applications, 2012, 134.
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10. Kumam P., “ Fixed point theorems for non expansive mappings in modular spaces”, Archivum Mathematicum, 2004, 40(4), 345 – 353.
11. Matthews S. G., “Partial metric topology,” Annals of the New York Academy of Sciences, 1994, 728, 183–197, Proc. 8th Summer Conference on General Topology and Applications.
12. Mustafa, Z., Sims, B. “A new approach to generalized metric spaces”, J. Nonlinear Convex, Anal. 2006, 7, 289–297.
13. Mustafa Z., Roshan J.R., Parvaneh V., “Coupled coincidence point results for (ψ, ϕ) −weakly contractive mappings in partially ordered Gb -metric spaces”. Fixed Point Theory Appl., 2013, 206.
14. Mustafa Z., Roshan J.R., Parvaneh V., “Existence of tripled coincidence point in ordered Gb -metric spaces and applications to a system of integral equations”. J. Inequal. Appl., 2013, 453.
15. Mustafa Z., Jaradat M.M.M., Aydi, H., Alrhayyel A., “Some common fixed points of six mappings on Gb -metric spaces using (E.A) property”. Eur. J. Pure Appl. Math., 2018, 11, 90–109.
16. Roshan J.R., Shobkolaei N., Sedghi S., Parvaneh V., Radenovi S. “Common fixed point theorems for three maps in discontinuous Gb -metric spaces”, Acta Math. Sci. Engl. Ser., 2014, 34, 1643–1654.
17. Sedghi S., Shobkolaei N., Roshan J.R., Shatanawi W., “Coupled fixed point theorems in Gb -metric spaces”, “ Matematiˇcki Vesnik, 2014, 66, 190–201.
18. Sintunavarat W., Kumam P., “Common fixed point theorem for hybrid generalized multi-valued contraction mappings”, Applied Mathematics Letters, 2012, 25, 52-57.
19. Sintunavarat W., Kumam P., “Coincidence and common fixed points for hybrid strict contractions without the weakly commuting condition”, Applied Mathematics Letters, 2009, 22(12), 1877-1881.
20. Sintunavarat W, Kumam P., “Common fixed point theorem for cyclic generalized multi-valued contraction mappings”, Applied Mathematics Letters , 2012, 25, 1849-1855.
21. Sintunavarat W., Cho Y. J., Kumam P., Coupled fixed point theorems for weak contraction mappings under F-invariant set, Abstract and Applied Analysis, 2012, Article ID 324874, 15 pages.
22. Yildirim I., Hojat Ansari A., “Some new fixed point results in b-metric spaces”, Topol. Algebra Appl., 2018, 6, 102–106.
2. Aydi H. , Abbas M. , Sintunavarat W., and Kumam P., “Tripled fixed point of W-compatible mappings in abstract metric spaces”, Fixed Point Theory and Applications, 2012, 134.
3. Bakhtin I.A., “The contraction mapping principle in almost metric space”, Function Anal, 1989, 30, 26–37.
4. Czerwik C., “Contraction mappings in b-metric spaces”, Acta Math. Inform. Univ. Ostrav, 1993, 1, 5–11.
5. Huang L.G., Zhang X., “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 2007, 332(2), 1468-1476.
6. Jaradat M.M.M., Mustafa, Z., Khan, S.U., Arshad, M., Ahmad, J, “Some fixed point results on G-metric and Gb -metric spaces”, Demonstr. Math., 2017, 207, 190–207.
7. Khojasteh F., Abbas M., Costache, “Two new types of fixed point theorems in complete metric spaces”, Abstract and Applied Analysis, 2014, Article ID 325840.
8. Khomdram B., Rohen Y., Singh T.C., “Coupled fixed point theorems in Gb -metric space satisfying some rational contractive conditions”. Springer Plus, 2016, 5, 1261.
9. Kumar J.,Vashistha, S., “Coupled fixed point theorems in complex valued Gb-metric spaces”. Adv. Fixed Point Theory, 2016, 6, 341–351.
10. Kumam P., “ Fixed point theorems for non expansive mappings in modular spaces”, Archivum Mathematicum, 2004, 40(4), 345 – 353.
11. Matthews S. G., “Partial metric topology,” Annals of the New York Academy of Sciences, 1994, 728, 183–197, Proc. 8th Summer Conference on General Topology and Applications.
12. Mustafa, Z., Sims, B. “A new approach to generalized metric spaces”, J. Nonlinear Convex, Anal. 2006, 7, 289–297.
13. Mustafa Z., Roshan J.R., Parvaneh V., “Coupled coincidence point results for (ψ, ϕ) −weakly contractive mappings in partially ordered Gb -metric spaces”. Fixed Point Theory Appl., 2013, 206.
14. Mustafa Z., Roshan J.R., Parvaneh V., “Existence of tripled coincidence point in ordered Gb -metric spaces and applications to a system of integral equations”. J. Inequal. Appl., 2013, 453.
15. Mustafa Z., Jaradat M.M.M., Aydi, H., Alrhayyel A., “Some common fixed points of six mappings on Gb -metric spaces using (E.A) property”. Eur. J. Pure Appl. Math., 2018, 11, 90–109.
16. Roshan J.R., Shobkolaei N., Sedghi S., Parvaneh V., Radenovi S. “Common fixed point theorems for three maps in discontinuous Gb -metric spaces”, Acta Math. Sci. Engl. Ser., 2014, 34, 1643–1654.
17. Sedghi S., Shobkolaei N., Roshan J.R., Shatanawi W., “Coupled fixed point theorems in Gb -metric spaces”, “ Matematiˇcki Vesnik, 2014, 66, 190–201.
18. Sintunavarat W., Kumam P., “Common fixed point theorem for hybrid generalized multi-valued contraction mappings”, Applied Mathematics Letters, 2012, 25, 52-57.
19. Sintunavarat W., Kumam P., “Coincidence and common fixed points for hybrid strict contractions without the weakly commuting condition”, Applied Mathematics Letters, 2009, 22(12), 1877-1881.
20. Sintunavarat W, Kumam P., “Common fixed point theorem for cyclic generalized multi-valued contraction mappings”, Applied Mathematics Letters , 2012, 25, 1849-1855.
21. Sintunavarat W., Cho Y. J., Kumam P., Coupled fixed point theorems for weak contraction mappings under F-invariant set, Abstract and Applied Analysis, 2012, Article ID 324874, 15 pages.
22. Yildirim I., Hojat Ansari A., “Some new fixed point results in b-metric spaces”, Topol. Algebra Appl., 2018, 6, 102–106.
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2025-02-08
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