Fixed point results in partially ordered partial $b_{v}(s)$-metric spaces

Document Type : Research Paper


Department of Mathematics, Faculty of Science, Erzurum Technical University, Erzurum, Turkey


In this paper, some fixed point results for generalized Geraghty type $α$-admissible contractive mappings and rational type generalized Geraghty contraction mappings are given in partially ordered partial  $b_{v}(s)$-metric spaces. Also, a modified version of a partial  $b_{v}(s)$-metric space is defined and a fixed point theorem is proved in this space. Finally, some examples are given related to the results.


[1] M. Abbas, I.Z. Chema and A. Razani, Existence of common fixed point for b-metric rational type contraction, Filomat 30(6) (2016) 1413–1429.
[2] A. Amini-Harandi and H. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and applications to ordinary differantial equations, Nonlinear Anal. 72 (2010) 2238–2242.
[3] M. Arshad, A. Hussaın, Fixed point results for generalized rational α-Geragty contraction, Miskolc Mat. Notes, 18 (2017) 611–621.
[4] S.E. Cho, J. S. Bae and E. Karapınar, Fixed Point theorems for α-Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl. 2013 Article ID 329 (2013).
[5] T. Dosenovic, Z. Kadelburg, Z. D. Mitrovic and S. Radenovic, New fixed point results in bv (s)-metric Spaces, Math. Slovaca, 70 (2020) 441–452.
[6] I. M. Erhan, Geraghty type contraction mappings on Branciari b-metric spaces, Adv. Theor. Nonlinear Anal. Appl. 1 (2017) 147–160.
[7] M. A. Geraghty, On contractive mappings, Proc. Amer. Math. Soc. 40 (1973) 604–608.
[8] M. Eshaghi Gordji and H. Habibi, Fixed point theory in ε-connected orthogonal metric space, Sahand Comm. Math. Anal. 16 (2019), 35–46.
[9] M. Eshaghi Gordji and H. Habibi, Fixed point theory in generalized orthogonal metric space, J. Linear Top. Alg. 6 (2017) 251–260.
[10] M. Eshaghi Gordji, H. Habibi and M. B. Sahabi, Orthogonal sets; orthogonal contractions, Asian-Eur. J. Math. 12 (2019) 1950034.
[11] M. Eshaghi Gordji, M. Ramezani, M. De La Sen and Y. J. Cho, On orthogonal sets and Banach fixed point theorem, Fixed Point Theory, 18(2) (2017) 569–578.
[12] M. Eshaghi Gordji, M. Ramezani, Y. J. Cho and S. Pirbavafa, A generalization of Geraghty’s theorem in partially ordered metricspaces and applications to ordinary differential equations, Fixed Point Theory Appl. 2012(74) (2012).
[13] I. Karahan and I. I¸sik, Partial bv (s), v-Generalized and bv (θ) metric spaces and related fixed point theorems, Facta Univ. Ser. Math. Inform. (In press).
[14] S. Khalehoghli, H. Rahimi and M. Eshaghi Gordji, Fixed point theorems in R-metric spaces with applications, AIMS Mathematics, 2020, 5(4): 3125-3137. doi: 10.3934/math.2020201.
[15] S. Khalehoghli, H. Rahimi and M. Eshaghi Gordji, R-topological spaces and SR-topological spaces with their applications, Math. Sci. 14 (2020) 249–255.
[16] A. Latif , J. R. Roshan, V. Parvaneh and N. Hussain, Fixed Point Results Via α-admissible mappings and cyclic contractive mappings in partial b-metric spaces, J. Inequal. Appl. 2014(345) (2014).
[17] S. G. Matthews, Partial metric topology, Ann. New York Acad. Sci. 728 (1994) 183–197.
[18] Z. D. Mitrovic and S. Radenovic, The Banach and Reich contractions in bv (s)-metric spaces, J. Fixed Point Theory Appl. 19 (2017) 3087–3095.
[19] Z. Mustafa, J. R. Roshan, V. Parvaneh and Z. Kadelburg, Some common fixed point results in ordered partial b-metric spaces, J. Inequal. Appl. 2013 (562) (2013).
[20] K. V. V. V. Prasad and A. K. Singh, Fixed point results for rational α-Geraghty contractive mappings, Adv. Inequal Appl. 1 (2019) (2019).
[21] J.R. Roshan , V. Parvaneh, Z. Kadelburg and N. Hussain, New Fixed Point Results in b-rectangular metric spaces, Nonlinear Anal. Model. Control 21 (5) (2016) 614-634.
[22] B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α−ψ-contractive mappings, Nonlinear Anal. 75 (2012) 2154–2165.
[23] S. Shukla, Partial b-metric spaces and fixed point theorems, Mediterr. J. Math., 11 (2014) 703–711.
[24] S. Shukla, Partial rectangular metric spaces and fixed point theorems, Sci. World J. Hindawi (2014) Article ID 756298 7 pages.
Volume 12, Issue 2
November 2021
Pages 35-52
  • Receive Date: 11 August 2020
  • Revise Date: 21 December 2020
  • Accept Date: 26 December 2020