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Suzuki-type fixed point theorems in relational metric spaces with applications. (English) Zbl 07890999

Summary: In this paper, we establish a relation-theoretic version of the results presented by J. K. Kim et al. [J. Nonlinear Convex Anal. 16, No. 9, 1779–1786 (2015; Zbl 1332.54212)]. To showcase the versatility of our results, we furnish some illustrative examples. Furthermore, we exhibit an application of our results to establish sufficient conditions for the existence of a positive definite common solution to a pair of nonlinear matrix equations.

MSC:

47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)

Citations:

Zbl 1332.54212
Full Text: DOI

References:

[1] A. Alam and M. Imdad, Relation-theoretic contraction principle, Journal of Fixed Point Theory and Applications, 17 (4) (2015), 693-702. · Zbl 1335.54040
[2] A. Alam and M. Imdad, Nonlinear contractions in metric spaces under locally t-transitive binary relations, Fixed Point Theory, 19 (1) (2018), 13-23. · Zbl 1460.54028
[3] S. Antal, D. Khantwal, S. Negi, and U. C. Gairola, Fixed points theorems for (φ, ψ, p)-weakly contractive mappings via w-distance in relational metric spaces with applica-tions, Filomat, 37 (21) (2023), 7319-7328.
[4] M. Arif and M. Imdad, Fixed point results under nonlinear Suzuki (F, R ̸ = )-contractions with an application, Filomat, 36 (9) (2022), 3155-3165.
[5] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae, 3 (1) (1922), 133-181. · JFM 48.0201.01
[6] A. Bartwal, R. C. Dimri, and S. Rawat, Fixed point results via altering distance functions in relational fuzzy metric spaces with application, Mathematica Moravica, 25 (2) (2021), 109-124. · Zbl 07803869
[7] M. Berzig, Solving a class of matrix equations via the Bhaskar-Lakshmikantham cou-pled fixed point theorem, Applied Mathematics Letters, 25 (11) (2012), 1638-1643. · Zbl 1252.15016
[8] M. Berzig and B. Samet, Solving systems of nonlinear matrix equations involving Lipshitzian mappings, Fixed Point Theory and Applications (2011), 89 (2011). · Zbl 1272.15011
[9] D. W. Boyd and J. S. W. Wong, On nonlinear contractions, Proceedings of the American Mathematical Society, 20 (1969), 458-464. · Zbl 0175.44903
[10] N. Chandra, B. Joshi and M. C. Joshi, Generalized fixed point theorems on metric spaces, Mathematica Moravica, 26 (2) (2022), 85-101. · Zbl 07804639
[11] U. C. Gairola and D. Khantwal, Suzuki type fixed point theorems in s-metric space, International Journal of Mathematics And its Applications, 5 (3-C) (2017), 277-289.
[12] A. Ghiura, Convergence analysis for Suzuki’s generalized nonexpansive mappings, Mathematica Moravica, (1) (2023), 13-22. · Zbl 07804645
[13] A. Hossain, M. Arif, S. Sessa and Q. H. Khan, Nonlinear relation-theoretic suzuki-generalized ćirić-type contractions and application to fractal spaces, Fractal and Frac-tional, 6 (12) (2022), 711.
[14] A. Hussain, M.Q. Iqbal and N. Hussain, Best proximity point results for suzuki-edelstein proximal contractions via auxiliary functions, Filomat, 33 (2) (2019), 435-447. · Zbl 1499.54175
[15] D. Khantwal, S. Aneja and U. C. Gairola, A generalization of Matkowski’s and Suzuki’s fixed point theorems, Asian-European Journal of Mathematics, 15 (9) (2022), Article ID: 2250169. · Zbl 1504.54033
[16] D. Khantwal, S. Antal and U. C. Gairola, Fixed point theorems to generalized FR-contraction mappings with applications to nonlinear matrix equations, Communica-tions Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70 (2) (2021), 631-652. · Zbl 1489.54158
[17] D. Khantwal, I. K. Letlhage and R. Pant, Fixed point results for Suzuki type contrac-tions in relational metric spaces with applications, Indian Journal of Mathematics, 64 (3) (2022), 279-304. · Zbl 07659995
[18] J. K. Kim, S. Sedghi and N. Shobkolaei, Suzuki-type of common fixed point theo-rems in metric spaces, Journal of Nonlinear and Convex Analysis, 16 (9) (2015), 1779-1786. · Zbl 1332.54212
[19] J. Long, X. Hu and L. Zhang, On the Hermitian positive definite solution of the nonlinear matrix equation X + A * X -1 A + B * X -1 B = I, Bulletin of the Brazilian Mathematical Society (N.S.), 39 (3) (2008), 371-386. · Zbl 1175.65052
[20] D. Paesano and P. Vetro, Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology and its Applications, 159 (3) (2012), 911-920. · Zbl 1241.54035
[21] R. Pant, Fixed point theorems for generalized semi-quasi contractions, Journal of Fixed Point Theory and Applications, 19 (2) (2017), 1581-1590. · Zbl 1456.54016
[22] R. Pant and S.N. Mishra, Stability results for suzuki contractions with an application to initial value problems, Filomat, 32 (9) (2018), 3297-3304. · Zbl 1491.54123
[23] G. Prasad, R. C. Dimri and A. Bartwal, Fixed points of Suzuki contractive mappings in relational metric spaces, Rendiconti del Circolo Matematico di Palermo (2), 69 (3) (2020), 1347-1358. · Zbl 1510.54041
[24] André C. M. Ran and M. C. B. Reurings, A fixed point theorem in partially or-dered sets and some applications to matrix equations, Proceedings of the American Mathematical Society, 132 (5) (2004), 1435-1443. · Zbl 1060.47056
[25] K. Sawangsup, W. Sintunavarat and A. F. R. L. de Hierro, Fixed point theorems for fr -contractions with applications to solution of nonlinear matrix equations, Journal of Fixed Point Theory and Applications, 19 (3) (2017), 1711-1725. · Zbl 1491.54153
[26] T. Senapati and L. K. Dey, Relation-theoretic metrical fixed-point results via w -distance with applications, Journal of Fixed Point Theory and Applications, 19 (4) (2017), 2945-2961. · Zbl 1489.54221
[27] S. Shil and H. K. Nashine, Unique positive definite solution of non-linear matrix equation on relational metric spaces, Fixed Point Theory, 24 (1) (2023), 367-382. · Zbl 07819961
[28] R. Shukla and R. Pant, Fixed point results for nonlinear contractions with application to integral equations, Asian-European Journal of Mathematics, 12 (7) (2019), Article ID: 2050007. · Zbl 07132431
[29] T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proceedings of the American Mathematical Society, 136 (5) (2008), 1861-1869. · Zbl 1145.54026
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