On unique and non-unique fixed point in parametric N_b−metric spaces with application

[1] I. A. Bakhtin, The contraction mapping principle in almost metric space, Functional analysis, 30 (Russian), Ulyanovsk. Gos. Ped. Inst., Ulyanovsk, (1989), 26–37. Search in Google Scholar

[2] S. Banach, Surles opérations dans les ensembles abstraits etleur applicationaux équations intégrales, Fundamenta Mathematicae, 3, (1922), 133181.10.4064/fm-3-1-133-181 Search in Google Scholar

[3] L. B. Ćirić, Generalised contractions and fixed-point theorems, Publ. Inst. Math., 12 (26), (1971), 9–26. Search in Google Scholar

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

[5] M. Fréchet, Sur quelques points du calcul fonctionnel, palemo, (30 via Ruggiero), (1906).10.1007/BF03018603 Search in Google Scholar

[6] M. Joshi, A. Tomar, and S. K. 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

[7] M. Joshi, A. Tomar, On unique and nonunique fixed points in metric spaces and application to Chemical Sciences, J. Funct. Spaces, 2021. https://doi.org/10.1155/2021/552547210.1155/2021/5525472 Search in Google Scholar

[8] M. Joshi, A. Tomar, H. A. Nabwey and R. George, On unique and nonunique fixed points and fixed circles in ℳvb \mathcal{M}_v^b -metric space and application to cantilever beam problem, J. Function Spaces, 2021: 15 p., (2021). https://doi.org/10.1155/2021/668104410.1155/2021/6681044 Search in Google Scholar

[9] M. Joshi, A. Tomar, and S. K. Padaliya, On geometric properties of non-unique fixed points in b−metric spaces, Chapter in the book “Fixed Point Theory and its Applications to Real World Problem” Nova Science Publishers, New York, USA., (2021), 33–50. ISBN:978-1-53619-336-7 Search in Google Scholar

[10] M. Joshi, A. Tomar, and S. K. Padaliya, Fixed point to fixed disc and application in partial metric spaces, Chapter in the book “Fixed point theory and its applications to real world problem” Nova Science Publishers, New York, USA., (2021), 391–406. ISBN:978-1-53619-336-7 Search in Google Scholar

[11] M. S. Khan, M. Swaleh, and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc., 30 (1), (1984), 1–9.10.1017/S0004972700001659 Search in Google Scholar

[12] N. Y. Özgür, Fixed-disc results via simulation functions, Turk. J. Math., 43, (2019), 2795–2805.10.3906/mat-1812-44 Search in Google Scholar

[13] B. Said, A. Tomar, A coincidence and common fixed point theorem for subsequentially continuous hybrid pairs of maps satisfying an implicit relation, Math. Morav. 21 (2), (2017), 15–25.10.5937/MatMor1702015B Search in Google Scholar

[14] B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for (α − ψ)−contractive type mappings, Nonlinear Anal., 75, (2012), 2154–2165.10.1016/j.na.2011.10.014 Search in Google Scholar

[15] S. Sedghi, N. Shobe, and T. Dosenovic, Fixed point results in 𝒮−metric spaces, Nonlinear Funct. Anal. Appl., 20 (1), (2015), 55–67. Search in Google Scholar

[16] S. Sedghi, A. Gholidahneh, T. Dosenovic, J. Esfahani, and S. Radenovic, Common fixed point of four maps in 𝒮_𝒷−metric spaces, J. Linear Topol. Algebra, 5(2016), 93–104. Search in Google Scholar

[17] S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorems in 𝒮−metric spaces, Mat. Vesnik, 64, (2012), 258–266.10.1186/1687-1812-2012-164 Search in Google Scholar

[18] W. Sintunavarat, Nonlinear integral equations with new admissibilty types in b−metric spaces, J. Fixed Point Theory Appl., doi10.1007/s11784-015-0276-6, (2017). Search in Google Scholar

[19] N. Souayah, N. Mlaiki, A fixed point theorem in Sb−metric space, J. Math., Computer Sci., 16, (2016), 131–139.10.22436/jmcs.016.02.01 Search in Google Scholar

[20] Tas, N. and Özgür, N.Y., On parametric S−metric spaces and fixed point type theorems for expansive mappings, J. Math., (2016).10.1155/2016/4746732 Search in Google Scholar

[21] N. Taş, and N. Y. Özgür, Some fixed point results on parametric N_b−metric spaces, Commu. Korean Math. Soc., 943–960, 33 (3), (2018), 943–960. Search in Google Scholar

[22] A. Tomar, and E. Karapinar, On variants of continuity and existence of fixed point via Meir-Keeler contractions in MC-spaces, J. Adv. Math. Stud., 9 (2), (2016), 348–359. Search in Google Scholar

[23] A. Tomar, R. Sharma, S. Beloul, and A. H. Ansari, C−class functions in generalized metric spaces and applications, J. Anal., (2019), 1–18.10.1007/s41478-019-00204-1 Search in Google Scholar

[24] 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 (14), (2019), 4655–4664.10.2298/FIL1914655T Search in Google Scholar

[25] A. Tomar, M. Joshi, M. and S. K. Padaliya, Fixed point to fixed circle and activation function in partial metric space, J. Appl. Anal., 28 (1), (2021), 2021–2057. https://doi.org/10.1515/jaa10.1515/jaa Search in Google Scholar

[26] A. Tomar and M. Joshi, Near fixed point, near fixed interval circle and near fixed interval disc in metric interval space, Chapter in the book “Fixed Point Theory and its Applications to Real World Problem” Nova Science Publishers, New York, USA., 131–150, 2021. ISBN: 978-1-53619-336-7 Search in Google Scholar

[27] A. Tomar, S. Beloul, R. Sharma, S. Upadhyay, Common fixed point theorems via generalized condition (B) in quasi-partial metric space and applications, Demonstr. Math., 50 (1), (2017), 278–298.10.1515/dema-2017-0028 Search in Google Scholar

[28] A. Tomar, Giniswamy, C. Jeyanthi, P. G. Maheshwari, On coincidence and common fixed point of six maps satisfying F−contractions, TWMS J. App. Eng. Math., 6 (2), (2016), 224–231. Search in Google Scholar

[29] A. Tomar, and R. Sharma, Almost alpha-Hardy-Rogers-F-contractions and applications, Armen. J. Math., 11 (11), (2019), 1–19.10.52737/18291163-2019.11.11-1-19 Search in Google Scholar

[30] M. Ughade, D. Turkoglu, S. K. Singh, R. D. Daheriya, Some fixed point theorems in Ab−metric space, British J. Math. & Computer Science 19 (6), (2016), 1–24.10.9734/BJMCS/2016/29828 Search in Google Scholar