Generalized Contractions on Extended \(b\)-Metric Space Endowed With a Graph
DOI:
https://doi.org/10.26713/cma.v13i3.1861Keywords:
Contraction, Fixed point, Extended b-metric space, GraphAbstract
The goal of this study is to obtain fixed point and coincidence point results for interpolative Hardy Rogers and Ćirić-Reich-Rus type contractive type mappings in an extended $b$-metric space, which is a generalization of \(b\)-metric space, based on Errai et al. (Some new results of interpolative Hardy-Rogers and Ćirić-Reich-Rus type contraction, 2021 (2021), Article ID 9992783). We present a variety of examples which backs up our findings.
Downloads
References
M. Abbas and G. Jungck, Common fixed point results for non commuting mappings without continuity in cone metric spaces, Journal of Mathematical Analysis and Applications 341(1) (2008), 416 – 420, DOI: 10.1016/j.jmaa.2007.09.070.
H. Afshari, H. Aydi and E. Karapınar, On generalized α-ψ-Geraghty contractions on b-metric spaces, Georgian Mathematical Journal 27(1) (2020), 9 – 21, DOI: 10.1515/gmj-2017-0063.
J. Ahmad, A. E. Al-Mazrooei, H. Aydi and M. De la Sen, On fixed point results in controlled metric spaces, Journal of Function Spaces 2020 (2020), Article ID 2108167, DOI: 10.1155/2020/2108167.
S. Aleksic, H. Huang, Z. D. Mitrovic and S. Radenovic, Remarks on some fixed point results in b-metric spaces, Journal of Fixed Point Theory and Applications 20 (2018), Article number: 147, DOI: 10.1007/s11784-018-0626-2.
M. A. Alghamdi, S. Gulyaz-Ozyurt and E. Karapınar, A note on extended Z-contraction, Mathematics 8(2) (2020), 195, DOI: 10.3390/math8020195.
H. Aydi, E. Karapinar and A. R. López de Hierro, ω-interpolative Ciric-Reich-Rus-type contractions, Mathematics 7(1) (2019), 57, DOI: 10.3390/math7010057.
A. Azam, N. Mehmood, J. Ahmad and S. Radenovic, Multivalued fixed point theorems in cone b-metric spaces, Journal of Inequalities and Applications 2013 (2013), Article number 582, DOI: 10.1186/1029-242X-2013-582.
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae 3(1) (1922), 133 – 181, DOI: 10.4064/fm-3-1-133-181.
I. Beg, A. R. Butt and S. Radojevic, The contraction principle for set-valued mapping on metric space with a graph, Computers & Mathematics with Applications 60(5) (2010), 1214 – 1219, DOI: 10.1016/j.camwa.2010.06.003.
F. Bojor, Fixed point of ϕ-contraction in metric spaces endowed with a graph, Annals of the University of Craiova, Mathematics and Computer Science Series 37 (4) (2010), 85 – 92, URL: http://inf.ucv.ro/~ami/index.php/ami/article/viewFile/374/338.
F. Bojor, Fixed points of Kannan mapping in metric spaces endowed with a graph, Analele stiintifice ale Universitatii “Ovidius” Constanta Seria Matematica 20(1) (20132), 31 – 40, DOI: 10.2478/v10309-012-0003-x.
S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis 1 (1993), 5 – 11, URL: https://dml.cz/bitstream/handle/10338.dmlcz/120469/ActaOstrav_01-1993-1_2.pdf.
P. Debnath and M. de La Sen, Fixed-points of interpolative Ciric-Reich-Rus-type contractions in b-metric spaces, Symmetry 12(1) (2020), 12, DOI: 10.3390/sym12010012.
D. Ðoric, Common fixed point for generalized (ψ,φ)-weak contractions, Applied Mathematics Letters 22(12) (2009), 1896 – 1900, DOI: 10.1016/j.aml.2009.08.001.
P. N. Dutta and B. S. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory and Applications 2008 (2008), Article ID 406368, DOI: 10.1155/2008/406368.
Y. Errai, El. M. Marhrani and M. Aamri, Some new results of interpolative Hardy-Rogers and Ciric-Reich-Rus type contraction, 2021 (2021), Article ID 9992783, 12 pages, DOI: 10.1155/2021/9992783.
Y. Errai, El M. Marhrani and M. Aamri, Related fixed point theorems in partially ordered b-metric spaces and applications to integral equations, Abstract and Applied Analysis 2021 (2021), Article ID 6672724, 14 pages, DOI: 10.1155/2021/6672724.
N. Hussain, A. Azam, J. Ahmad and M. Arshad, Common fixed point results in complex valued metric space with applications to system of integral equations, Filomat 28(7) (2014), 1363 – 1380, DOI: 10.2298/fil1407363h.
J. Jachymski, The contraction principle for mappings on a metric space with a graph, American Mathematical Society 136(4) (2007), 1359 – 1373, URL: https://www.ams.org/journals/proc/2008-136-04/S0002-9939-07-09110-1/S0002-9939-07-09110-1.pdf.
T. Kamran, M. Samreen and Q. Ul Ain, A generalization of b-metric space and some fixed point theorems, Mathematics 5(2) (2017), 19, DOI: 10.3390/math5020019.
R. Kannan, Some results on fixed points, Bulletin Calcutta Mathematical Society 60 (1968), 71 – 76.
N. Mlaiki, H. Aydi, N. Souayah and T. Abdeljawad, Controlled metric type spaces and the related contraction principle, Mathematics 6(10) (2018), 194, DOI: 10.3390/math6100194.
S. K. Panda, A. Tassaddiq and R. P. Agarwal, A new approach to the solution of non-linear integral equations via various FBe -contractions, Symmetry 11(2) (2019), 206, DOI: 10.3390/sym11020206.
A. Petru¸sel and G. Petru¸sel, Fixed point results for multi-valued locally contractive operators, Applied Set-Valued Analysis and Optimization 2(2) (2020), 175 – 181, DOI: 10.23952/asvao.2.2020.2.04.
M. Samreen and T. Kamran, Fixed point theorems for weakly contractive mappings on a metric space endowed with a graph, Filomat 28(3) (2014), 441 – 450, DOI: 10.2298/fil1403441s.
W. Sintunavarat, Fixed point results in b-metric spaces approach to the existence of a solution for nonlinear integral equations, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 110(2) (2016), 585 – 600, DOI: 10.1007/s13398-015-0251-5.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
