Abstract
The ambition of this paper is to construct fixed point theorems fulfilling a generalized locally F-contractive multivalued mapping on a closed ball in complete b-metric-like space. Example and application are given to show the novelty of our results. Our results combine, extend and infer several comparable results in the existing literature.
Similar content being viewed by others
References
Abbas, M., Ali, B., Romaguera, S.: Fixed and periodic points of generalized contractions in metric spaces. Fixed Point Theory Appl. 2013, 243 (2013)
Acar, Ö., Altun, I.: A fixed point theorem for multivalued mappings with \(\delta\)-distance. Abstr. Appl. Anal. 5, Article ID 497092 (2014)
Acar, Ö., Durmaz, G., Minak, G.: Generalized multivalued \(F\)-contractions on complete metric spaces. Bull. Iran. Math. Soc. 40, 1469–1478 (2014)
Ahmad, J., Al-Rawashdeh, A., Azam, A.: Some new fixed Point theorems for generalized contractions in complete metric spaces. Fixed Point Theory Appl. 2015, 80 (2015)
Ameer, E., Arshad, M.: Two new generalization for \(F\)-contraction on closed ball and fixed point theorem with application. J. Math. Exten. 11, 1–24 (2017)
Aydi, H., Bota, M. F., Karapinar, E., Mitrovi’c, S.: Fixed point theorem for set-valued quasi-contractions in b-metric spaces. Fixed Point Theory Appl 88 (2012)
Banach, S.: Sur les opérations dans les ensembles abstraits et leur application aux equations itegrales. Fund. Math. 3, 133–181 (1922)
Bojor, F.: Fixed point theorems for Reich type contraction on metric spaces with a graph. Nonlinear Anal. 75, 3895–3901 (2012)
Boriceanu, M.: Fixed Point theory for multivalued generalized contraction on a set with two b-metrics. Studia Univ Babes Bolya: Math. LIV 3, 1–14 (2009)
Chen, C., Wen, L., Dong, J., Gu, Y.: Fixed point theorems for generalized \(F\)-contractions in b-metric-like spaces. J. Nonlinear Sci. Appl. 9, 2161–2174 (2016)
Czerwik, S.: Contraction mappings in b-metric spaces. Acta Math. Inform. Univ. Ostraviensis 1, 511 (1993)
Gholamian, N.: Fixed points of generalized \(\alpha\)-Meir–Keeler type contractions and Meir–Keeler contractions through rational expression in b-metriclike spaces. J. Linear Topol. Algebra 9(1), 17–34 (2020)
Hussain, N., Roshan, J. R., Paravench, V., Abbas, M.: Common Fixed Point results for weak contractive mappings in ordered dislocated b-metric space with applications. J. Inequal. Appl 2013, 486 (2013). https://doi.org/10.1186/1029-242X-2013-
Isik, H., Parvaneh, V., Mohammadi, B., Altun, I.: Common fixed point results for generalized Wardowski type contractive multivalued mappings. Mathematics 7(11), 1130 (2019)
Isik, H., Mohammadi, B., Haddadi, M.R., Parvaneh, V.: On a new generalization of Banach contraction principle with application. Mathematics 7(9), 862 (2019)
Kadelburg, Z., Radenović, S.: Notes on some recent papers concerning \(F\)-contractions in \(b\)-metric spaces. Constr. Math. Anal. 1(2), 108–112 (2018)
Mahmood, Q., Shoaib, A., Rasham, T., Arshad, M.: Fixed point results for the family of multivalued \(F\)-contractive mappings on closed ball in complete dislocated \(b\)-metric spaces. Mathematics 7(1), 56 (2019). https://doi.org/10.3390/math7010056
Nadler, S.B.: Multivalued contraction mappings. Pac. J. Math. 30, 475–488 (1969)
Parvaneh, V., Hussain, N., Khorshidi, M., Mlaiki, N., Aydi, H.: Fixed point results for generalized \(F\)-contractions in modular \(b\)-metric spaces with applications. Mathematics 7(10), 887 (2019). https://doi.org/10.3390/math7100887
Parvaneh, V., Hussain, N., Kadelburg, Z.: Generalized Wardowski type fixed point theorems via alpha-admissible \(FG\)-contractions in \(b\)-metric spaces. Acta Mathematica Scientia 36(5), 1445–1456 (2016)
Piri, H., Kumam, P.: Some fixed point theorems concerning \(F\)-contraction in complete metric spaces. Fixed Point Theory Appl. 2014, 210 (2014)
Piri, H., Rahrovi, S., Morasi, H., Kumam, P.: Fixed point theorem for \(F\)-Khan-contractions on complete metric spaces and application to the integral equations. J. Nonlinear Sci. Appl. 10, 4564–4573 (2017)
Rasham, T., Shoaib, A., Alamri, B.A.S., Arshad, M.: Multivalued fixed point results for new generalized \(F\)-dominated contractive mappings on dislocated metric space with application. J. Funct. Spaces 2018 , 12 (2018), Article ID 4808764
Rasham, T., Shoaib, A., Hussain, N., Arshad, M., Khan, S.U.: Common fixed point results for new Ciric-type rational multivalued \(F\)-contraction with an application. J. Fixed Point Theory Appl. 20(1), 20–45 (2018)
Rasham, T., Marino, G., Shoaib, A.: Fixed points for a pair of \(F\)-dominated contractive mappings in rectangular b-metric spaces with graph. Mathematics 7(10), 884 (2019). https://doi.org/10.3390/math7100884
Rasham, T., Shoaib, A., Alamri, B.A.S., Arshad, M.: Common fixed point results for two families of multivalued \(A\)-dominated contractive mappings on closed ball with applications. Open Math. 17, 1350–1360 (2019)
Rasham, T., Shoaib, A., Marino, G., Alamri, B.A.S., Arshad, M.: Sufficient conditions to solve two systems of integral equations via fixed point results. J. Inequal. Appl. 2019, 182 (2019). https://doi.org/10.1186/s13660-019-2130-7
Rasham, T., Shoaib, A., Hussain, N., Alamri, B.A.S., Arshad, M.: Multivalued fixed point results in dislocated \(b\)-metric spaces with application to the system of nonlinear integral equations. Symmetry 11(1), 40 (2019). https://doi.org/10.3390/sym11010040
Secelean, N. A.: Iterated function systems consisting of \(F\)-contractions. Fixed Point Theory Appl. 2013, Article ID 277 (2013). https://doi.org/10.1186/1687-1812-2013-277.
Sen, M.D.l, Nikolić, N., Došenović, T., Pavlovi ć, M., Radenović, S.: Some results on (s-q)-graphic contraction mappings in \(b\)-metric-like spaces. Mathematics 7, 1190 (2019). https://doi.org/10.3390/math7121190
Sgroi, M., Vetro, C.: Multi-valued \(F\)-contractions and the solution of certain functional and integral equations. Filomat 27(7), 1259–1268 (2013)
Shukla, S., Radenović, S., Vetro, C.: Set-valued Hardy-Rogers type contraction in 0-complete partial metric spaces. Int. J. Math. Math. Sci. 2014, 5, Article ID 652925 (2014)
Wardowski, D.: Fixed point theory of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl. 2012, Article ID 94 (2012)
Acknowledgements
The authors would like to thank the Editor, the Associate Editor and the anonymous referees for sparing their valuable time for reviewing this article.
Author information
Authors and Affiliations
Contributions
Each author equally contributed to this paper, read and approved the final manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Rasham, T., Shoaib, A., Zaman, Q. et al. Fixed point results for a generalized F-contractive mapping on closed ball with application. Math Sci 14, 177–184 (2020). https://doi.org/10.1007/s40096-020-00329-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40096-020-00329-6