Riv. Mat. Univ. Parma, Vol. 12, No. 2, 2021

Mohamed Abdalla [a,b], Zahia Mostefaoui [c] and Fuli He [d]

Some fixed point results in ordered bicomplex-valued metric spaces
Pages: 201-219
Received: 6 March 2020
Accepted in revised form: 11 February 2021
Mathematics Subject Classification: 47H10, 54D99, 54E99.
Keywords: Bicomplex numbers, Partial order, Fixed point, Contraction mapping, Compatible mapping.
Authors address:
[a]:Mathematics Department, Faculty of Science, King Khalid University, Abha 61471, Saudi Arabia.
[b]:Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt.
[c]:Department of Mathematics, E.N.S, B.P. 92 Vieux Kouba, 16050 Algiers, Algeria.
[d]:School of Mathematics and Statistics, Central South University, Changsha 410083, China.

Full Text (PDF)

This research was supported by Deanship of Scientific Research at King Khalid University.
Abstract: Recently, fixed point results on bicomplex valued metric spaces have had many applications in functional analysis, graph theory, probability theory and other areas. Very recently, Fuli He et al. (J. Funct. Spaces, 2020, Art. ID 4070324) introduced fixed point theorems for Mizoguchi-Takahashi type contraction in bicomplex-valued metric spaces and applications. In this direction of research, we demonstrate some fixed point theorems in ordered bicomplex valued metric spaces for type contraction mappings with illustrative examples. The reported results here along with those stated in earlier papers were also specified.

References
[1]
P. Agarwal, M. Jleli and B. Samet, Fixed point theory in metric spaces, Recent advances and applications, Springer, Singapore, 2018. MR3887557
[2]
R. P. Agarwal, M. Meehan and D. O'Regan, Fixed point theory and applications, Cambridge Tracts in Math., 141, Cambridge University Press, Cambridge, 2001. MR1825411
[3]
D. Alpay, M. E. Luna-Elizarrarás, M. Shapiro and D. Struppa, Basics of functional analysis with bicomplex scalars, and bicomplex Schur analysis, SpringerBriefs Math., Springer, Cham, 2014. MR3309382
[4]
A. M. Zidan and A. Al Rwaily, On new type of F-contractive mapping for quasipartial b-metric spaces and some results of fixed-point theorem and application, J. Math. 2020, Art. 8825805, 8 pp. MR4189669
[5]
A. H. Soliman and A. M. Zidan, Existential examination of the coupled fixed point in generalized b-metric spaces and an application, J. Intell. Fuzzy Systems 38 (2020), 2801-2807. DOI
[6]
A. H. Soliman, T. Nabil and A. M. Zidan, On quasi-partial generalized type of metric spaces and an application to complexity analysis of computer algorithms, Alex. Engin. J. 59 (2020), 1233-1238. DOI
[7]
A. H. Soliman and A. M. Zidan, A new coupled fixed point result in extended metric spaces with an application to study the stability of set-valued functional equations, J. Funct. Spaces 2019, Art. 4146328, 6 pp. MR4050897
[8]
S. Chandok, Some common fixed point results for rational type contraction mappings in partially ordered metric spaces, Math. Bohem. 138 (2013), 407-413.  Article
[9]
A. Azam, B. Fisher and M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim 32 (2011), 243-253. MR2748327
[10]
J. Choi, S. K. Datta, T. Biswas and M. N. Islam, Some fixed point theorems in connection with two weakly compatible mappings in bicomplex valued metric spaces, Honam Math. J. 39 (2017), 115-126. MR3676679
[11]
D. Gopal, P. Kumam and M. Abbas, eds., Background and Recent Developments of metric fixed point theory, CRC Press, Boca Raton, FL, 2018. MR3791477
[12]
F. He, Z. Mostefaoui and M. Abdalla, Fixed point theorems for Mizoguchi-Takahashi type contraction in bicomplex-valued metric spaces and applications, J. Funct. Spaces 2020 Art. 4070324, 7 pp. MR4109863
[13]
M. E. Luna-Elizarrarás, M. Shapiro, D. C. Struppa and A. Vajiac, Bicomplex holomorphic functions, The algebra, geometry and analysis of bicomplex numbers, Frontiers in Mathematics, Birkhäuser/Springer, Cham, 2015. MR3410909
[14]
R. Gervais Lavoie, L. Marchildon and D. Rochon, Finite-dimensional bicomplex Hilbert spaces, Adv. Appl. Clifford Algebr. 21 (2011), 561-581. MR2825022
[15]
I. H. Jebril, S. K. Datta, R. Sarkar and N. Biswas, Common fixed point theorems under rational contractions for a pair of mappings in bicomplex valued metric spaces, J. Interdiscip. Math. 22 (2019), 1071-1082. DOI
[16]
G. B. Price, An introduction to multicomplex spaces and functions, Monogr. Textbooks Pure Appl. Math., 140, Marcel Dekker, New York, 1991. MR1094818
[17]
N. Singh, D. Singh, A. Badal and V. Joshi, Fixed point theorems in complex valued metric spaces, J. Egyptian Math. Soc. 24 (2016), 402-409. MR3509869

Home Riv.Mat.Univ.Parma