Browse > Article
http://dx.doi.org/10.22771/nfaa.2022.27.02.06

A COMMON FIXED POINT THEOREM IN AN M*-METRIC SPACE AND AN APPLICATION  

Gharib, Gharib M. (Department of Mathematics, Faculty of Science Zarqa University)
Malkawi, Abed Al-Rahman M. (Department of Mathematics, Faculty of Science The University of Jordan, Department of Mathematics, Faculty of Sciences and Literature Jordan University of Science and Technology)
Rabaiah, Ayat M. (Department of Mathematics, Faculty of Science The University of Jordan)
Shatanawi, Wasfi A. (Department of General Sciences Prince Sultan University, Department of Mathematics Hashemite University)
Alsauodi, Maha S. (Department of Mathematics, Faculty of Science The University of Jordan)
Publication Information
Nonlinear Functional Analysis and Applications / v.27, no.2, 2022 , pp. 289-308 More about this Journal
Abstract
In this paper, we introduce the concept of M*-metric spaces and how much the M*-metric and the b-metric spaces are related. Moreover, we introduce some ways of generating M*-metric spaces. Also, we investigate some types of convergence associated with M*-metric spaces. Some common fixed point for contraction and generalized contraction mappings in M*-metric spaces. Our work has been supported by many examples and an application.
Keywords
D-metric space; b-metric space; common fixed point;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 N. Hussain, D. DoriL, Z. Kadelburg and S. RadenoviLc., Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., 2012 2012:126, doi:10.1186/1687-1812-2012-126..   DOI
2 A. Aghajani, M. Abbas and J.R. Roshan, common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64 (2014), 941-960.   DOI
3 C. Alegre, A. Fulga, E. Karapinar and P. Tirado, A discussion on p-geraghty contraction on mw-quasi-metric spaces, Mathematics, 2020, 8, 1437; doi:10.3390/math8091437.   DOI
4 H. Aydi, M. Bota, E. Karapinar and S. Moradi, A common fixed point for weak 𝜙-contractions on b-metric spaces, Fixed Point Theory Appl., 13(2) (2012), 337-346.
5 I.A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal., 30 (1989), 26-37.
6 M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Modern Math., 4(3) (2009), 285-301.
7 S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostra. 1(1993), 5-11.
8 R. George, A. Belhenniche, S. Benahmed, Z. Mitrovi, N. Mlaiki and L. Guran , On an open question in controlled rectangular b-metric spaces, Mathematics, 8 (2020), 2239, doi:10.3390.   DOI
9 N. Hussain and M.H. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl., 62 (2011), 1677-1684.   DOI
10 E. Ghasab, H. Majani, E. Karapinar and G. Rad, New fixed point results in F-quasi-metric spaces and an application, Advances in Math. Phys. 2020, Article ID 9452350, 6 pages.
11 E. Karapiner, F. Khojasteh and W. Shatanawi, Revisiting Ciric-type contraction with Caristis approach, Symmetry, 11(6) (2019):726.   DOI
12 E. Karapinar, S. Moustafa, A. Shehata and R. Agarwal, Fractional hybrid differential equations and coupled fixed point results for α-admissible F(𝜓1, 𝜓2)-contractions in Mmetric spaces, Hindawi Disc. Dyn. Natu. Soc.,2020 (2020), Article ID 7126045, 13 pages.
13 A. Malkawi, A. Rabaiah, W. Shatanawi and A. Talafhah, MR-metric spaces and an application, (2021), preprint.
14 A. Malkawi, A. Tallafha and W. Shatanawi, Coincidence and fixed point results for (𝜓, L)-M-weak contraction mapping on MR-metric spaces, Italian J. Pure Appl. Math., accepted (2020).
15 A. Bataihah, W. Shatanawi, T. Qawasmeh and R. Hatamleh, On 𝓗-simulation functions and fixed point results in the setting of ωt-distance mappings with application on matrix equations, Mathematics, 8 (2020), 837. https://www.mdpi.com/2227-7390/8/5/837.   DOI
16 H. Afshari and E. Karapnar, Afshari and Karapnar Advances in Difference Equations A discussion on the existence of positive solutions of the boundary value problems via 𝜓-Hilfer fractional derivative on b-metric spaces, Springier open Journal, 20:616.
17 M. Boriceanu, Fixed point theory for multivalued generalized contractions on a set with two b-metric, Creative Math Inf., 17 (2008), 326-332.
18 N. Mlaiki, N. Ozguz, A. Mukhelmer and N. Tas, A New extension of the Mb-metric spaces, J. Math. Anal., 9 (2018), 118-133.
19 Z. Mustafa, J.R. Roshan and V. Parvaneh, Coupled Coincidence Point results for (𝜓, 𝜙)-weakly counteractive mappings in Partially ordered Gb-metric Spaces, Fixed Point Theory Appl., 2013 2013:206.   DOI
20 M. Pacurar, Sequences of almost contractions and fixed points in b-metric spaces, Analele Universitatii de Vest, Timisoara Seria Matematica Informatica, XLVIII., 3 (2010), 125-137.
21 M. Boriceanu, M. Bota, A. Petrusel, Multivalued fractals in b-metric spaces, Cent. Eur. J. Math., bf 8 (2010), 367-377.
22 B.C. Dhage, Generalized metric spaces and topological structure I, Analene Stint, Univ. "Al.I, cuza" Iasi., 45 (2000), 3-24.
23 H. Huang and S.H. Xu, Fixed point theorems of contractive mappings in cone b-metric spaces and applications, Fixed Point Theory Appl., 2013 2013:112.   DOI
24 E. Karapinar, F. Khojasteh, Z. Mitrovic and V. Rakocevic, On surrounding quasicontractions on non-triangular metric spaces, Open Mathematics, 18 (2020), 11131121.
25 M.A. Khamsi and N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal., 73 (2010), 3123-3129.   DOI
26 A. Rabaiah, A. Tallafha and W. Shatanawi, Common fixed point results for mappings under nonlinear contraction of cyclic form in MR-metric spaces, Nonlinear Funct. Anal. Appl., 26(2) (2021), 289-301.   DOI
27 A. Malkawi, A. Tallafha and W. Shatanawi, Coincidence and fixed point results for generalized weak contraction mapping on b-metric spaces. Nonlinear Funct. Anal. Appl., 26(1) (2021), 177-195,   DOI
28 M. Pacurar, A fixed point results for 𝜙-contraction on b-metric spaces without the boundedness assumption, Fasciculi Math., 43 (2010), 127-136.
29 V. Parvaneh, J.R. Roshan and S. Radenovic, Existence of tripled coincidence points in ordered b-metric spaces and an application to a system of integral equations, Fixed Point Theory Appl., 2013 2013:130.   DOI
30 T. Qawasmeh, A new contraction based on H -simulation functions and fixed point results in theframe of extended b-metric spaces and application, Inter. J. Electrical Comp. Eng., Accepted.
31 S.V.R. Naidu, K. Rao and N. Srinivasa Rao, On the topology of D-metric spaces and the generalization of D-metric spaces from metric spaces, Int. J. Math. Math. Sci., 51 (2004), 2719-2740.
32 A. Rabaiah, A. Tallafha and W. Shatanawi, Common fixed point results for mappings under nonlinear contraction of cyclic form in b-metric spaces, Adv. Math. Sci. J., accepted (2020).
33 H. Aydi, M. Bota, E. Karapnar and S. Mitrovic, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl., 88 (2012) 2012, doi:10.1186/1687-1812-2012-88.   DOI
34 B.C. Dhage, Generalized metric spaces and topological structure II, Pure. Appl. Math. Sci., 40(1-2) (1994), 37-412.
35 J.R. Roshan, N. Shobkolaei, S. Sedghi and M. Abbas, Common fixed point of four maps in b-metric spaces, Hacettepe J. Math. Stat., 43 (2014), 613-624.
36 H. Saleh, S. Sessa, W. Alfaqih, M. Imdad, and N. Mlaiki, Fixed circle and fixed disc results for new types of Θc-contractive mappings in metric spaces, Symmetry, 2012 (2012:12), 1825; doi:10.3390/sym12111825.   DOI
37 W. Shatanawi, A. Pitra and R. Lazovi, Contraction conditions using comparison functions on b-metric spaces, Fixed Point Theory Appl., 2013, 2013:120.   DOI
38 T. Qawasmeh, W. Shatanawi, A. Bataihah and A. Tallafha, Fixed point results and (α, β)-triangular admissibility in the frame of complete extended b-metric spaces and application, U.P.B. Sci. Bull., Series A, 83(1) (2021), 113-124.