×

Common fixed point theorem for multivalued mappings using ternary relation in \(G\)-metric space with an application. (English) Zbl 1497.54080

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
54E40 Special maps on metric spaces
54E50 Complete metric spaces
54C60 Set-valued maps in general topology
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Nadler, S. B., Multi-valued contraction mappings, Pacific Journal of Mathematics, 30, 2, 475-488 (1969) · Zbl 0187.45002
[2] Banach, S., Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae, 3, 1, 133-181 (1922) · JFM 48.0201.01
[3] Kaneko, H.; Sessa, S., Fixed point theorems for compatible multi-valued and single-valued mappings, International Journal of Mathematics and Mathematical Sciences, 12, 2 (1989) · Zbl 0671.54023
[4] Jungck, G., Commuting mappings and fixed points, The American Mathematical Monthly, 83, 4, 261-263 (1976) · Zbl 0321.54025
[5] Kubiak, T., Fixed points for contractive type multi-functions, Mathematica Japonica, 30, 89-101 (1985) · Zbl 0567.54030
[6] Pathak, H. K., Fixed point theorems for weak compatible multi-valued and single valued mappings, Acta Mathematica Hungarica, 67, 1-2, 69-78 (1995) · Zbl 0821.54027
[7] Mustafa, Z.; Sims, B., Fixed point theorems for contractive mappings in complete \(G\)-metric spaces, Fixed Point Theory and Applications, 2009 (2009) · Zbl 1179.54067
[8] Mustafa, Z.; Sims, B., A new approach to generalised metric spaces, Journal of Non-linear and Convex Analysis, 7, 2, 289-297 (2006) · Zbl 1111.54025
[9] Abbas, M.; Rhoades, B. E., Common fixed point results for non-commuting mappings without continuity in generalized metric spaces, Applied Mathematics and Computation, 215, 1, 262-269 (2009) · Zbl 1185.54037
[10] Kaewcharoen, A.; Kaewkhao, A., Common fixed points for single-valued and multi-valued mappings in \(G\)-metric spaces, International Journal of Mathematical Analysis, 5, 36, 1775-1790 (2011) · Zbl 1246.54042
[11] 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 and Applications, 2012 (2012) · Zbl 1273.54078
[12] Mustafa, Z.; Arshad, M.; Khan, S. U.; Ahmad, J.; Jaradat, M. M. M., Common fixed points for multivalued mappings in \(G\)-metric spaces with applications, Journal of Nonlinear Sciences and Applications, 10, 2550-2564 (2017) · Zbl 1412.47154
[13] Shoaib, A.; Shahzad, A., Common fixed point of multivalued mappings in ordered dislocated quasi \(G\)-metric spaces, Punjab University Journal of Mathematics, 52, 10 (2020)
[14] Alam, A.; Imdad, M., Relation-theoretic contraction principle, Journal of Fixed Point Theory and Applications, 17, 4, 693-702 (2015) · Zbl 1335.54040
[15] Ahmadullah, M.; Ali, J.; Imdad, M., Unified relation-theoretic metrical fixed point theorems under an implicit contractive condition with an application, Fixed Point Theory and Applications, 2016, 1 (2016) · Zbl 1505.54058
[16] Ahmadullah, M.; Imdad, M.; Gubran, R., Relation-theoretic metrical fixed point theorems under nonlinear contractions (2016), https://arxiv.org/abs/1611.04136
[17] Ahmadullah, M.; Khan, A. R.; Imdad, M., Relation-theoretic contraction principle in metric-like as well as partial metric spaces (2016), https://arxiv.org/abs/1612.05521
[18] Eke, K. S.; Davvaz, B.; Oghonyon, J. G., Relation-theoretic common fixed point theorems for a pair of implicit contractive maps in metric spaces, Communications in Mathematics and Applications, 10, 1, 159-168 (2019)
[19] Kolman, B.; Busby, R. C.; Ross, S., Discrete Mathematical Structures, 2000 (2000), New Delhi: PHI Pvt. Ltd., New Delhi
[20] Samet, B.; Turinici, M., Fixed point theorems on a metric space endowed with an arbitrary binary relation and applications, Communications in Mathematical Analysis, 13, 2, 82-97 (2012) · Zbl 1259.54024
[21] Perveen, A.; Khan, I. A.; Imdad, M., Relation theoretic common fixed point results for generalized weak nonlinear contractions with an application, Axioms, 8, 2, 49 (2019) · Zbl 1432.54074
[22] Hossain, A.; Khan, F. A.; Khan, Q. A., A relation-theoretic metrical fixed point theorem for rational type contraction mapping with an application, Axioms, 10, 4, 316 (2021)
[23] Gaba, Y. U.; Agyingi, C. A.; Choudhury, B. S.; Maity, P., Generalized Banach contraction mapping principle in generalized metric spaces with a ternary relation, Surveys in Mathematics and its Applications, 2019, 14, 159-171 (2019) · Zbl 1438.54125
[24] Radha, M. K.; Singh, B., A novel approach to \(G\)-metric spaces by using ternary relations, International Journal of Pure and Applied Mathematical Sciences, 14, 1, 29-38 (2021)
[25] Badshah, V. H.; Bhagat, P.; Shukla, S., Some common fixed point theorems for contractive mappings in cone 2-metric spaces equipped with a ternary relation, International Journal of Pure and Applied Mathematical Sciences, 14, 1, 29-38 (2021) · Zbl 1474.54121
[26] Agarwal, P.; Mohamed, J.; Samet, B., Fixed Point Theory in Metric Spaces, Recent Advances and Applications (2018), Springer · Zbl 1416.54001
[27] Vetro, C.; Vetro, F., Common fixed points of mappings satisfying implicit relations in partial metric spaces, Journal of Nonlinear Science and Applications, 6, 3, 152-161 (2013) · Zbl 1432.54086
[28] Nová, V.; Novotný, M., Transitive ternary relations and quasiorderings, Archivum Mathematicum, 25, 1, 5-12 (1989) · Zbl 0714.06001
[29] NovotnỲ, M., Ternary structures and groupoids, Czechoslovak Mathematical Journal, 41, 1, 90-98 (1991) · Zbl 0790.20090
[30] Šlapal, J., Relations and topologies, Czechoslovak Mathematical Journal, 43, 1, 141-150 (1993) · Zbl 0797.04002
[31] Lipschutz, S., Schaum’s Outline of Theory and Problems of Set Theory and Related Topics (1964), MCGraw-Hill
[32] Anitar, T.; Ritu, S., Some coincidence and common fixed point theorems concerning \(F\)-contraction and applications, Journal of International Mathematical Virtual Institute, 2018, 8, 181-198 (2018) · Zbl 1449.54101
[33] Saipara, P.; Khammahawong, K.; Kumam, P., Fixed-point theorem for a generalized almost Hardy-Rogers-type \(F\)-contraction on metric-like spaces, Mathematical Methods in the Applied Sciences, 42, 17, 5898-5919 (2019) · Zbl 1489.54212
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.