Certain new type of fixed point results in partially ordered M-metric space

Document Type : Research Paper


1 Department of Mathematics and Statistics, International Islamic University Islamabad, Pakistan

2 Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore, Pakistan

3 Head of International Relations, IIMS Pune, India


The most recent performances in fixed point theory related to the fixed point, coincidence point, and coupled coincidence point involving mappings in ordered metric spaces are the result of concentrated overwork ordered metric space. Its conclusion was expansive and generalized to well-known oral literature results. A few fixed point outcomes were discovered to be sophisticated self-mappings. Anything that satisfies a generalized week contraction was partially ordered as m-metric space (mms). The specific results also include two self-mappings for coupling coincidence points, coupled common fixed points, and coincidence points in the same qualification. An example is offered to support the findings.


[1] M. Asadi, E. Karapinar and P. Salimi, New extension of p-metric spaces with some fixed-points results on M-metric spaces, J. Inequal. Appl. 18 (2014), 1–9.
[2] M. Asadi, M. Azhini, E. Karapinar and H. Monfared, Simulation functions over M-metric spaces, East Asian Math. J. 33 (2017), 559–570.
[3] M. Asim, A.R. Khan and M. Imdad, Rectangular Mb-metric spaces and fixed point results, J. Math. Anal. 10 (2019), 10–18.
[4] M. Asim, K.S. Nisar, A. Morsy and M. Imdad, Extended rectangular Mr-metric spaces and fixed point results, Mathematics 7 (2019), 1136.
[5] M. Asim, I. Uddin and M. Imdad, Fixed point results in Mv-metric spaces with an application, J. Inequal. Appl. 2019 (2019), 1–19.
[6] M. Aslanta¸s, H. Sahin and D. Turkoglu, Some Caristi type fixed point theorems, J. Anal. 29 (2020), 89–103.
[7] S. Banach, Sur les oprations dans les ensembles abstraits et leur application aux quations intgrales, Fund. Math. 3 (1922), 131–181.
[8] D.W. Boyd and J.S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458–464.
[9] S.K. Chatterjee, Fixed point theorems, C. R. Acad. Bulgare Sci. 25 (1972), 727–730.
[10] L.B. Ciri´c, Generalized contractions and fixed point theorems, Publ. Inst. Math. 12 (1971), 19–26.
[11] L.B. Ciri´c, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45 (1974), 267–273.
[12] F.U. Din, M. Din, U. Ishtiaq, and S. Sessa, Perov fixed-point results on F-contraction mappings equipped with binary relation, Mathematics 11 (2023), no. 1, 238.
[13] R. Kannan, Some results on fixed points, Bull. Cal. Math. 60 (1968), 71–76.
[14] U. Ishtiaq, M. Asif, A. Hussain, K. Ahmad, I. Saleem, and H. Al Sulami, Extension of a unique solution in generalized neutrosophic cone metric spaces, Symmetry 15 (2022), no. 1, 94.
[15] U. Ishtiaq, N. Saleem, F. Uddin, S. Sessa, K. Ahmad, and F. di Martino, Graphical views of intuitionistic fuzzy double-controlled metric-like spaces and certain fixed-point results with application, Symmetry 14 (2022), no. 11, 2364.
[16] Z. Kadelburg and S. Radenovi´c, Notes on some recent papers concerning F-contractions in b-metric spaces, Constr. Math. Anal. 1 (2018), 108–112.
[17] S. Luambano, S. Kumar and G. Kakiko, Fixed point theorem for F-contraction mappings in partial metric spaces, Lobachevskii J. Math. 40 (2019), 183–188.
[18] G. Minak, A. Helvaci and I. Altun, Ciri´c type generalized F-contractions on complete metric spaces and fixed point results, Filomat 28 (2014), 1143–1151.
[19] H. Monfared, M. Azhini and M. Asadi, A generalized contraction principle with control function on M-metric spaces, Nonlinear Funct. Anal. Appl. 22 (2017), 395–402.
[20] W. Onsod, P. Kumam and Y. J. Cho, Fixed points of α − θ- Geraghty type and θ- Geraghty graphic type contractions, Appl. Gen. Topol. 18 (2017), 153–171.
[21] H. Piri and P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl. 2014 (2014), 210.
[22] H. Piri, S. Rahrovi, H. Marasi and P. Kumam, F-contraction on asymmetric metric spaces, J. Math. Comput. Sci. 17 (2017), 32–40.
[23] S. Reich, Some remarks concerning contraction mappings, Canad. Math. Bull. 14 (1971), 121–124.
[24] H. Sahin, A new type of F-contraction and their best proximity point results with homotopy application, Acta Appl. Math. 179 (2022), 1–15.
[25] H. Sahin, I. Altun and D. Turkoglu, Two fixed point results for multivalued F contractions on M-metric spaces, Rev. R. Acad. Cienc. Exactas Fıs. Nat. Ser. A Mat. RACSAM 113 (2019), 1839–1849.
[26] S. Shukla, Partial rectangular metric spaces and fixed point theorems, Sci. World J. 2014 (2014).
[27] T. Suzuki, Generalized distance and existence theorems in complete metric spaces, J. Math. Anal. Appl. 253 (2001), 440–458.
[28] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012 (2012), 1–6.
[29] T. Zamfirescu, Fixed point theorems in metric spaces, Arch. Math. 23 (1972), 292–298.
Volume 14, Issue 4
April 2023
Pages 193-205
  • Receive Date: 06 February 2023
  • Accept Date: 20 March 2023