Fixed Point Results for (ψ, ϕ)-Contractive Mapping in GF-Metric Space

Kapil Jain, Jatinderdeep Kaur, Satvinder Singh Bhatia

Abstract


The main goal of this work is to present GF -metric space, a new generalization of G-metric space. A comparison between the classes of G-metric spaces, GP-metric spaces, Gb-metric spaces, generalized Gb-metric spaces, and G∗ -metric spaces and the class of GF - metric spaces is also presented. We examine a few fundamental aspects of this newly defined abstract space. Proving the Banach contraction principle and the fixed point result for (ψ, ϕ)-contractive mapping in the context of GF -metric spaces is the paper’s secondary goal

Keywords


Fixed point; complete metric space; G-metric space; Gb-metric space; F-metric space; Cauchy sequence

Full Text:

PDF

References


Mustafa, Z.; and Sims, B.; (2006), A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis, 7, 289-297.

G¨ahler, S.; (1963), 2 Metrische R¨ame und Ihr Topological Struktur, Mathematische Nachrichten, 26, 115-148.

Dhage, B.C.; (1992), Generalized metric spaces and mappings with fixed point, Bulletinof the Calcutta Mathematical Society, 84, 329-336.

Mustafa, Z.; (2005), A new structure for generalized metric spaces with applications to fixed point theory, Ph.D. Thesis, The University of Newcastle, Callaghan, Australia.

Mustafa, Z.; Obiedat, H.; and Awawdeh, F.; (2008), Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory and Applications, article ID 189870, doi: 10.1155/2008/189870.

Mustafa, Z.; Shatanawi, W.; and Bataineh, M.; (2009), Existence of fixed point results in G-metric spaces, International Journal of Mathematics and Mathematical Sciences, article ID 283028, 10 pages, doi: 10.1155/2009/283028.

Mustafa, Z.; and Sims, B.; (2009), Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory and Applications, article ID 917175, doi: 10.1155/2009/917175.

Mustafa, Z.; Awawdeh, F.; and Shatanawi, W.; (2010), Fixed point theorem for expansive mappings in G-metric spaces, International Journal of Contemporary Mathematical Sciences, 5, 2463-2472.

Jleli, M.; and Samet, B.; (2012), Remarks on G-metric spaces and fixed point theorems, Fixed Point Theory and Applications, 2012:210.

Asadi, M.; Karapinar, E.; and Salimi, P.; (2013), A new approach to G-metric and related fixed point theorems, Journal of Inequalities and Applications, 2013:454.

Karapinar, E.; and Aggarwal, R.P.; (2013), Further fixed point results on G-metric spaces, Fixed Point Theory and Applications, 2013:154.

Mustafa, Z.; Arshad, M.; Khan, S.U.; Ahmad, J.; and Jaradat, M.M.M.; (2017), Commmon fixed points for multivalued mappings in G-metric spaces with applications, Journal of Nonlinear Sciences and Applications, doi: 10.22436/jnsa.010.05.23.

Matthews, G.S.; (1992), Partial metric topology, Research Report 212, Deptt. of Computer Science, University of Warwick.

Zand, M.R.A.; and Nezhad, A.D.; (2011), A generalization of partial metric spaces,Journal of Contemporary Applied Mathematics, 24, 86-93.

Parvaneh, V.; Roshan, J.R.; and Kadelburg, Z.; (2013), On generalized weakly Gpcontractive mappings in ordered Gp-metric spaces, Gulf Journal of Mathematics, 1, 78-97.

Aydi, H.; Karapinar, E.; and Salimi, P.; (2012), Some fixed point results in Gp-metric spaces, Journal of Applied Mathematics, 2012, 16 pages, article ID 891713.

Bilgili, N.; Karapinar, E.; and Salimi, P.; (2013), Fixed point theorems for generalized contractions on Gp-metric spaces, Fixed Point Theory and Applications, 2013:317.

Ciric, Lj.; Alsulami, S.M.; Parvaneh, V.; and Roshan, J.R.; (2013), Some fixed point results in ordered Gp-metric spaces, Fixed Point Theory and Applications, 2013:317.

Barakat, M.A.; and Zidan, A.M.; (2015), A common fixed point theorem for weak contractive maps in Gp-metric spaces, Journal of Egptian Mathematical Society, 23, 309-314.

Popa, V.; and Patriciu, A.M.; (2015), Two general fixed point theorems for a sequence of mappings satisfying implicit relation in Gp-metric spaces, Applied General Topology, 16(2), 225-231.

Ansari, A.H.; Vetro, P.; and Radenovic, S.; (2017), Existence of fixed point for GP(Λ,Θ)-contractive mappings in Gp-metric spaces, Filomat, 31(8), 2211-2218. doi: 10.2298/FIL1708211A.

Gajic, L.; Kadelburg, Z.; and Radenovic, S.; (2017), Gp-metric spaces−symmetric and asymmetric, University of Novi Paza Series A Applied Mathematics Informatics and Mechanics, 9(1), 37-46.

Yazdi, H.G.; Zand, M.R.A.; and Radenovic, S.; (2018), Coupled fixed point on Gpmetric spaces−symmetric and asymmetric, Advances and Applications of Mathematical Sciences, 17(10), 681-692.

Popa, V.; (2020), A general fixed point theorem for two pairs of absorbing mappings in Gp-metric spaces, Annales Mathematicae Silesianae, doi: 10.2478/amsil-2020-0004.

Aghajani, A.; Abbas, M.; and Roshan, J.R.; (2014), Common fixed point of generalized weak contractive mappings in partially ordered Gb-metric spaces, Filomat, 28:6, 1087-1101, doi: 10.2298/Fil1406087A.

Czerwik, S.; (1998), Nonlinear set-valued contraction mapping in b-metric spaces, Atti del Seminaro Matematico e Fisico dell’Universita di Modena e Reeggio Emilia, 46, 263-276.

Mustafa, Z.; Roshan, J.R.; and Parvaneh, V.; (2013), Coupled coincidence point results for (ψ, ϕ)-weakly contractive mappings in partially ordered Gb-metric spaces, Fixed Point Theory and Applications, 2013, 206.

Roshan, J.R.; Shobkolaei, N.; Sedghi, S.; Parvaneh V. and Radenovic, S.; (2014), Common fixed point theorems for three maps in discontinuous Gb-metric spaces, Acta Mathematica Scientia, 34B(5), 1643-1654.

Sedghi, S.; Shobkolaei, N.; Roshan J.R.; and Shatanawi, W.; (2014), Coupled fixed point theorems in Gb-metric spaces, Matematicki Vesnik, 66(2):190-201.

Shahkoohi, R.J.; Kazemipour, S.A.; and Eyvali, A.R.; (2014), Tripled coincidence point under ϕ-contractions in ordered Gb-metric spaces, Journal of Linear and Topological Algebra, 03(03), 131-147.

Khomdram, B.; Rohen, Y.; and Singh, T.C.; (2016), Coupled fixed point theorems in Gb-metric space satisfying some rational contractive conditions, SpringerPlus, 5, 1261.

Kumar, J.; and Vashistha, S.; (2016), Coupled fixed point theorems in complex-valued Gb-metric spaces, Advances in Fixed Point Theory, 6:341-351.

Jaradat, M.M.M.; Mustafa, Z.; Khan, S.U.; Arshad, M.; and Ahmad, J.; (2017) Some fixed point results on G-metric and Gb-metric spaces, Demonstratio Mathematica, 207: 190-207.

Mustafa, Z.; Jaradat, M.M.M.; Aydi, H.; and Alrhayyel, A.; (2018), Some common fixed points of six mappings on Gb-metric spaces using (E.A) property, European Journal of Pure and Applied Mathematics, 11:90-109.

Aydi, H.; Rakic, D.; Aghajani, A.; Dosenovic, T.; Noorani, M.S.M.; and Qawaqneh, H.; (2019), On fixed point results in Gb-metric spaces, Mathematics, 7(7):617.

Ege, O.; Park, C.; and Ansari, A.H.; (2020), A different approach to complex valued Gb-metric spaces, Advances in Difference Equations, 2020:152.

Gupta, V.; Ege, O.; Saini, R.; and Sen, M.D.L.; (2021), Various fixed point results in complete Gb-metric spaces, Dynamic Systems and Applications, 30(2), 277-293.

Wangwe, L.; (2022), Coincidence fixed point theorems for p-hybrid contraction mappings in Gb-metric space with application, Abstract and Applied Analysis, Article ID 7688168, 13 pages.

Jain, K.; and Kaur, J.; (2019), A generalization of G-metric spaces and related fixed point theorems, Mathematical Inequalities and Applications, 22, 1145-1160.

Jain, K.; Kaur, J.; and Bhatia, S.S.; (2022), A generalization of GP-metric space and generalized Gb-metric space and related fixed point results, Journal of Mathematical and Computational Science, 12, 27 pages, Article ID 132.

Jleli, M.; and Samet, B.; (2018), On a new generalization of metric spaces, Journal of Fixed Point Theory and Application, 20, 128.

Alnaser, L.A.; Lateef, D., Fouad, H.A., and Ahmad, J.; (2019), Relational theoretic contraction results in F-metric spaces, Journal of Nonlinear Sciences and Applications, 12, 337-344, doi: 10.22436/jnsa.012.05.06.

Bera, A., Garai, H., Damjanovi´c, B., and Chanda, A.; (2019), Some interesing results on F-metric spaces, Filomat, 33:10, 3257-3268, doi: 10.2298/FIL1910257B.

Lateef, D., and Ahmad, J.; (2019), Dass and Gupta’s fixed point theorem in F-metric spaces, Journal of Nonlinear Sciences and Applications, 12, 405-411, doi: 10.22436/jnsa.012.06.06.

Mitrovi´c, Z.D., Aydi, H., Hussain, N., and Mukheimer, A.; (2019), Reich, Jungck, and Berinde common fixed point results in F-metric spaces and an application, Mathematics, 7, 387, 10 pages, doi: 10.3390/math7050387.

Altun, I., and Erduran, A.; (2022), Two fixed point results on F-metric spaces, Topological Algebra and its Applications, 10, 61-67, doi: 10.1515/taa-2022-0114.

Dutta, P.N.; and Choudhary, B.S.; (2008), A generalization of contraction principle in metric spaces, Fixed Point Theory and Applications, Article ID 406368.

Doric, D.; (2009), Common fixed point for generalized (ψ, ϕ)-weak contraction, Applied Mathematics Letters, Article ID 406368.

Aghajani, A.; Abbas, M.; and Roshan, J.R.; (2014), Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Mathematica Slovaca, 64(4), 941-960, doi: 10.2478/s12175-014-0250-6.

Rao, N.S; and Kalyani, K; (2022), Fixed point results for (ψ, ϕ)-weak contractions in ordered b-metric spaces, CUBO, A Mathematical Journal, 24(2), 343-368, doi:10.56754/0719-0646.2402.0343.




DOI: http://dx.doi.org/10.23755/rm.v51i0.1455

Refbacks

  • There are currently no refbacks.


Copyright (c) 2024 KAPIL JAIN, Jatinderdeep Kaur, Satvinder Singh Bhatia

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.