Common Fixed Point Theorems in Extended Rectangular b-Metric Spaces
About this article
Abstract
In this paper, we establish common fixed point theorems for quadruple weakly compatible mappings satisfying a new generalized contraction condition. Our results generalize the corresponding result of Budi Nurwahyu et al. [6]. Non-trivial examples are further provided to support the hypotheses of our results.
Keywords
- Compatible mapping
- Common Fixed point
- Extended rectangular b-metric
- Fixed point
- Weak contraction mapping
References
[1] N. Alamgir, Q. Kiran, H. Aydi , A. Mukheimer, “A Mizoguchi–Takahashi type fixed point theorem in complete extended b-metric spaces”, Mathematics, 7(5), (2019), 1 − 15, DOI:10.3390/math7050478.
[2] B. Alqahtani, A, Fulga, E. Karapınar, “Common fixed point results on an extended b-metric space”, J Inequalities and Appl, 2018(1), 1 − 15, https://doi.org/10.1186/s13660-018-1745-4.
[3] M. Asim, M. Imdad, S. Radenovic, “Fixed point results in extended rectangular b-metric spaces with an Application”, University Politehnica of Bucharest Scientific Bulletin-Series A-Applied Mathematics and Physics, 81(2, )(2019), 43 − 50.
[4] I. A. Bakhtin, “The contraction mapping principle in almost metric space”, Funct Anal Gos Ped Inst Unianowsk, 30(1989), 26-37.
[5] S. Banach, “Sur les op’erationsdans les ensembles abstraits et leur application aux’equations int’egrales”, Fund. Math., 3, (1922), 133-181.
View more references (23)
[6] B. Nurwahyu, M. S. Khan, N. Fabiano, S. Radenovic, “Common Fixed Point on generalized weak contraction mappings in extended rectangular b-Metric Spaces”, Faculty of Sciences and Mathematics, University of Niˇs, Serbia, 35(11)(2021), 3621 − 3634, DOI:10.2298/FIL2111621N.
[7] L. Ciric, “Some Results in Metrical Fixed Point Theory”, University of Belgrade, Beograd 2003, Serbia.
[8] S. Czerwik, “Acta Mathematica et Informatica Universitatis Ostraviensis”, 1 (1), (1993), 5-11.
[9] M. Demma, P. Vetro, “Picard Sequence and Fixed Point Results on b-Metric Spaces”, Journal of Function Spaces (2)2015, 1 − 6, DOI:10.1155/2015/189861.
[10] P. N. Dutta, B. S. .A Choudhury, “A generalization of contraction principle in metric spaces”, Fixed Point Theory and Appl 2008(1), 1 − 8, doi:10.1155/2008/406368.
[11] R. George, S. Radenovic, K. P. Reshma, S. Shukla, “Rectangular b-metric space and contraction principles”, J Nonlinear Sci Appl, 8(2015), 1005-1013.
[12] N. Hussain, V. Parvaneh, B. S. A. Alamri, Z. Kadelburg, “F-HR-type contractions on (α, η)-complete rectangular b-metric spaces”, J Nonlinear Sci Appl, 10(3),(2017), 1030-1043, doi:10.22436/jnsa.010.03.14.
[13] M. Jleli, E. Karapınar, B. Samet, “Further generalizations of the Banach contraction principle”, J Inequalities and Appl, 2014(1), 1-9.
[14] G. Jungck, “Compatible mappings and common fixed points” International J Math and Math Sci, 9(4), (1986), 771-779.
[15] Z. Kadelburg, S. Radenovic, “Pata-type common fixed point results in b-metric and b-rectangular metric spaces”, J Nonlinear Sci Appl, 8(6), (2015), 944-954, DOI:10.22436/jnsa.008.06.05.
[16] T. Kamran, M. Samreen, Q. UL Ain, “A generalization of b-metric space and some fixed point theorems”, Mathematics, 5(2), (2017), 1-7, doi:10.3390/math502001.
[17] H. Lakzian, B. Samet, “Fixed points for (Ψ, Φ)-weakly contractive mappings in generalized metric spaces”, Applied Mathematics Letters, 25(5), (2012), 902-906, https://doi.org/10.1016/j.aml.2011.10.047.
[18] J. Merryfield, J. D. Stein Jr, “A generalization of the Banach contraction principle”, J Math Anal and Appl, 273(1), (2002), 112-120.
[19] P. K. Mishra, S. Sachdeva, S. K. Banerjee, “Some fixed point theorems in b-metric space”, Turkish J Analysis and Number Theory, 2(1), (2014), 19-22, DOI: 10.12691/tjant-2-1-5.
[20] Z. D. Mitrovic, “A note on a Banach’s fixed point theorem in b-rectangular metric space and b-metric space”, Mathematica Slovaca, 68(5), (2018), 1113-1116, DOI:10.1515/ms-2017-0172.
[21] Z. D. Mitrovic, H. Isik, S. Radenovic, “The new results in extended b-metric spaces and applications”, Int. J. Nonlinear Anal. Appl., 11 (2020), 473-482, http://dx.doi.org/10.22075/ijnaa.2019.18239.1998.
[22] Z. Mustafa, V. Parvaneh, M M Jaradat, Z. Kadelburg, “Extended rectangular b-metric spaces and some fixed point theorems for contractive mappings”, Symmetry 11(4), (2019), 1-17, https://doi.org/10.3390/sym11040594.
[23] B. E. Rhoades, “Some theorems on weakly contractive maps”, Nonlinear Analysis: Theory, Methods and Appl, 47(4), (2001), 2683-2693, https://doi.org/10.1016/S0362-546X(01)00388-1.
[24] M. Samreen, T. Kamran, “Fixed point theorems for weakly contractive mappings on a metric space endowed with a graph”, Filomat, 28(3), (2014), 441-450.
[25] W. Shatanawi, K. Abodayeh, A. Mukheimer, “Some fixed point theorems in extended b-metric spaces”, Politehn Univ Bucharest Sci Bul Ser A Appl Math Phys, 80(2018), 71-78.
[26] T. Suzuki, “A generalized Banach contraction principle that characterizes metric completeness”, Proc of the American Math Soc, 136(5), (2008), 1861-1869.
[27] N. Van Luong, N. X. Thuan, “Fixed point theorem for generalized weak contractions satisfying rational expressions in ordered metric spaces”, Fixed Point Theory and App, 2011(1), 1-10.
[28] V. T. Cevic, “Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics”, Springer Nature Switzerland AG, 2019, 1-163.