Relation theoretic contractions and their applications in b-metric like spaces

References

[1] A. Alam and M. Imdad, Relation-theoretic contraction principle, J. Fixed Point Theory Appl. 17 (2015), no. 4, 693–702. 10.1007/s11784-015-0247-ySearch in Google Scholar

[2] A. Alam and M. Imdad, Relation-theoretic metrical coincidence theorems, Filomat 31 (2017), no. 14, 4421–4439. 10.2298/FIL1714421ASearch in Google Scholar

[3] M. A. Alghamdi, N. Hussain and P. Salimi, Fixed point and coupled fixed point theorems on b-metric-like spaces, J. Inequal. Appl. 2013 (2013), Paper No. 402. 10.1186/1029-242X-2013-402Search in Google Scholar

[4] A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl. 2012 (2012), Paper No. 204. 10.1186/1687-1812-2012-204Search in Google Scholar

[5] I. A. Bakhtin, The contraction mapping principle in almost metric space, Funct. Anal. 30 (1989), 26–37. Search in Google Scholar

[6] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922), 133–181. 10.4064/fm-3-1-133-181Search in Google Scholar

[7] D. W. Boyd and J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458–464. 10.1090/S0002-9939-1969-0239559-9Search in Google Scholar

[8] F. E. Browder, On the convergence of successive approximations for nonlinear functional equations, Nederl. Akad. Wetensch. Proc. Ser. A 71 30 (1968), 27–35. 10.1016/S1385-7258(68)50004-0Search in Google Scholar

[9] T. A. Burton, Integral equations, implicit functions, and fixed points, Proc. Amer. Math. Soc. 124 (1996), no. 8, 2383–2390. 10.1090/S0002-9939-96-03533-2Search in Google Scholar

[10] L. Ćirić, A new fixed-point theorem for contractive mappings, Publ. Inst. Math. (Beograd) (N. S.) 30(44) (1981), 25–27. Search in Google Scholar

[11] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis 1 (1993), 5–11. Search in Google Scholar

[12] W. L. de Koning, Infinite horizon optimal control of linear discrete time systems with stochastic parameters, Automatica J. IFAC 18 (1982), no. 4, 443–453. 10.1016/0005-1098(82)90072-3Search in Google Scholar

[13] J. Dugundji, Positive definite functions and coincidences, Fund. Math. 90 (1975/76), no. 2, 131–142. 10.4064/fm-90-2-131-142Search in Google Scholar

[14] J. Dugundji and A. Granas, Weakly contractive maps and elementary domain invariance theorem, Bull. Soc. Math. Grèce (N. S.) 19 (1978), no. 1, 141–151. Search in Google Scholar

[15] M. Fréchet, Sur quelques points du calcul fonctionnel, Rend. Circ. Mat. Palermo 22 (1906), 1–72. 10.1007/BF03018603Search in Google Scholar

[16] M. A. Geraghty, On contractive mappings, Proc. Amer. Math. Soc. 40 (1973), 604–608. 10.1090/S0002-9939-1973-0334176-5Search in Google Scholar

[17] M. A. Geraghty, An improved criterion for fixed points of contraction mappings, J. Math. Anal. Appl. 48 (1974), 811–817. 10.1016/0022-247X(74)90155-3Search in Google Scholar

[18] N. Gholamian and M. Khanehgir, Fixed points of generalized Meir-Keeler contraction mappings in b-metric-like spaces, Fixed Point Theory Appl. 2016 (2016), Paper No. 34. 10.1186/s13663-016-0507-6Search in Google Scholar

[19] J. A. Górnicki, Remarks on contractive type mappings, Fixed Point Theory Appl. 2017 (2017), Paper No. 8. 10.1186/s13663-017-0601-4Search in Google Scholar

[20] H. A. Hammad and M. De la Sen, Generalized contractive mappings and related results in b - metric like spaces with an application, Symmetry 11 (2019), 10.3390/sym11050667. 10.3390/sym11050667Search in Google Scholar

[21] J. Jachymski, Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl. 194 (1995), no. 1, 293–303. 10.1006/jmaa.1995.1299Search in Google Scholar

[22] M. Joshi, A. Tomar and SK Padaliya, Fixed Point to Fixed Ellipse in Metric Spaces and Discontinuous Activation Function, Appl. Math. E-Notes 21 (2021), 225–237. Search in Google Scholar

[23] B. Kolman, R. C. Busby and S. Ross, Discrete Mathematical Structures, 3rd ed., PHI Pvt., New Delhi, 2000. Search in Google Scholar

[24] M. A. Kutbi, A. Roldán, W. Sintunavarat, J. Martínez-Moreno and C. Roldán, F-closed sets and coupled fixed point theorems without the mixed monotone property, Fixed Point Theory Appl. 2013 (2013), Paper No. 330. 10.1186/1687-1812-2013-330Search in Google Scholar

[25] J. Liouville, Second Mémoire sur le développement des functions ou parties de functions en series dont divers terms sont assujettis á satisfaire a une meme equation différentielle du second ordre contenant unparamétre variable, J. Math. Pure Appl. 2 (1837), 16–35. Search in Google Scholar

[26] R. D. Maddux, Relation Algebras, Stud. Logic Found. Math. 150, Elsevier, Amsterdam, 2006. Search in Google Scholar

[27] S. Manro and A. Tomar, Common fixed point theorems using property (EA) and its variants involving quadratic terms, Annals of Fuzzy Mathematics and Informatics 7 (2014), no. 3, 473–484. Search in Google Scholar

[28] J. Matkowski, Fixed point theorems for contractive mappings in metric spaces, Časopis Pěst. Mat. 105 (1980), no. 4, 341–344, 409. 10.21136/CPM.1980.108246Search in Google Scholar

[29] S. G. Matthews, Partial metric topology, Papers on General Topology and Applications (Flushing 1992), Ann. New York Acad. Sci. 728, New York Academy of Sciences, New York (1994), 183–197. 10.1111/j.1749-6632.1994.tb44144.xSearch in Google Scholar

[30] A. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 28 (1969), 326–329. 10.1016/0022-247X(69)90031-6Search in Google Scholar

[31] S. Lipschutz, Schaum’s Outlines of Theory and Problems of Set Theory and Related Topics, McGraw-Hill Book, New York, 1964. Search in Google Scholar

[32] A. Mukherjea, Contractions and completely continuous mappings, Nonlinear Anal. 1 (1976/77), no. 3, 235–247. 10.1016/0362-546X(77)90033-5Search in Google Scholar

[33] E. Picard, Mémoire sur la théorie des équations aux dérivées partielles et la méthode des approximations successives, J. Math. Pures Appl. 6 (1890), 145–210. Search in Google Scholar

[34] B. E. Rhoades, Contractive definitions and continuity, Fixed Point Theory and its Applications (Berkeley 1986), Contemp. Math. 72, American Mathematical Society, Providence (1988), 233–245. 10.1090/conm/072/956495Search in Google Scholar

[35] A.-F. Roldán-López-de Hierro, A unified version of Ran and Reuring’s theorem and Nieto and Rodríguez–López’s theorem and low-dimensional generalizations, Appl. Math. Inf. Sci. 10 (2016), no. 2, 383–393. 10.18576/amis/100201Search in Google Scholar

[36] B. Samet and M. Turinici, Fixed point theorems on a metric space endowed with an arbitrary binary relation and applications, Commun. Math. Anal. 13 (2012), no. 2, 82–97. Search in Google Scholar

[37] B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Anal. 75 (2012), no. 4, 2154–2165. 10.1016/j.na.2011.10.014Search in Google Scholar

[38] B. Samet, C. Vetro and H. Yazidi, A fixed point theorem for a Meir–Keeler type contraction through rational expression, J. Nonlinear Sci. Appl. 6 (2013), no. 3, 162–169. 10.22436/jnsa.006.03.02Search in Google Scholar

[39] S. Shukla, Partial b-metric spaces and fixed point theorems, Mediterr. J. Math. 11 (2014), no. 2, 703–711. 10.1007/s00009-013-0327-4Search in Google Scholar

[40] M. R. Tasković, A generalization of Banach’s contraction principle, Publ. Inst. Math. (Beograd) (N. S.) 23(37) (1978), 179–191. Search in Google Scholar

[41] A. Tomar and M. Joshi, Relation-theoretic nonlinear contractions in an ℱ -metric space and applications, Rend. Circ. Mat. Palermo (2) 70 (2021), no. 2, 835–852. 10.1007/s12215-020-00528-zSearch in Google Scholar

[42] A. Tomar and R. Sharma, Some coincidence and common fixed point theorems concerning F-contraction and applications, J. Internat. Math. Virtual Institute 8 (2018), 181–198. Search in Google Scholar

[43] A. Tomar, Giniswamy, C. Jeyanthi and PG. Maheshwari, Coincidence and common fixed point of F-contractions via C ⁢ L ⁢ R S ⁢ T property, Surveys in Mathematics and its Applications 11 (2016), 21–31. Search in Google Scholar

[44] A. Tomar, M. Joshi, S. K. Padaliya, B. Joshi and A. Diwedi, Fixed point under set-valued relation-theoretic nonlinear contractions and application, Filomat 33 (2019), no. 14, 4655–4664. 10.2298/FIL1914655TSearch in Google Scholar