Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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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)
  • Received : 2021.09.24
  • Accepted : 2021.12.07
  • Published : 2022.06.08
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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

References

  1. 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.
  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. https://doi.org/10.2478/s12175-014-0250-6
  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.
  4. 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.
  5. 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.
  6. I.A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal., 30 (1989), 26-37.
  7. 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. https://doi.org/10.3390/math8050837
  8. M. Boriceanu, Fixed point theory for multivalued generalized contractions on a set with two b-metric, Creative Math Inf., 17 (2008), 326-332.
  9. M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Modern Math., 4(3) (2009), 285-301.
  10. M. Boriceanu, M. Bota, A. Petrusel, Multivalued fractals in b-metric spaces, Cent. Eur. J. Math., bf 8 (2010), 367-377.
  11. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostra. 1(1993), 5-11.
  12. B.C. Dhage, Generalized metric spaces and topological structure II, Pure. Appl. Math. Sci., 40(1-2) (1994), 37-412.
  13. B.C. Dhage, Generalized metric spaces and topological structure I, Analene Stint, Univ. "Al.I, cuza" Iasi., 45 (2000), 3-24.
  14. 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. https://doi.org/10.3390/math8122239
  15. 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.
  16. 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. https://doi.org/10.1186/1687-1812-2013-112
  17. 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..
  18. N. Hussain and M.H. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl., 62 (2011), 1677-1684. https://doi.org/10.1016/j.camwa.2011.06.004
  19. E. Karapinar, F. Khojasteh, Z. Mitrovic and V. Rakocevic, On surrounding quasicontractions on non-triangular metric spaces, Open Mathematics, 18 (2020), 11131121.
  20. E. Karapiner, F. Khojasteh and W. Shatanawi, Revisiting Ciric-type contraction with Caristis approach, Symmetry, 11(6) (2019):726. https://doi.org/10.3390/sym11060726
  21. 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.
  22. M.A. Khamsi and N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal., 73 (2010), 3123-3129. https://doi.org/10.1016/j.na.2010.06.084
  23. A. Malkawi, A. Rabaiah, W. Shatanawi and A. Talafhah, MR-metric spaces and an application, (2021), preprint.
  24. 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).
  25. 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, https://doi.org/10.22771/NFAA.2021.26.01.13
  26. N. Mlaiki, N. Ozguz, A. Mukhelmer and N. Tas, A New extension of the Mb-metric spaces, J. Math. Anal., 9 (2018), 118-133.
  27. 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. https://doi.org/10.1186/1687-1812-2013-206
  28. 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.
  29. 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.
  30. M. Pacurar, A fixed point results for 𝜙-contraction on b-metric spaces without the boundedness assumption, Fasciculi Math., 43 (2010), 127-136.
  31. 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. https://doi.org/10.1186/1687-1812-2013-130
  32. 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.
  33. 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.
  34. 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).
  35. 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. https://doi.org/10.22771/NFAA.2021.26.02.04
  36. 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.
  37. 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.
  38. W. Shatanawi, A. Pitra and R. Lazovi, Contraction conditions using comparison functions on b-metric spaces, Fixed Point Theory Appl., 2013, 2013:120. https://doi.org/10.1186/1687-1812-2013-120