Gnanaprakasam, Arul Joseph; Boulaaras, Salah Mahmoud; Mani, Gunaseelan; Cherif, Bahri; Idris, Sahar Ahmed Solving system of linear equations via bicomplex valued metric space. (English) Zbl 07473384 Demonstr. Math. 54, 474-487 (2021). Summary: In this paper, we prove some common fixed point theorems on bicomplex metric space. Our results generalize and expand some of the literature’s well-known results. We also explore some of the applications of our key results. MSC: 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 47H10 Fixed-point theorems 30G35 Functions of hypercomplex variables and generalized variables 46N99 Miscellaneous applications of functional analysis 54H25 Fixed-point and coincidence theorems (topological aspects) Keywords:bicomplex valued metric space; common fixed point linear equation PDFBibTeX XMLCite \textit{A. J. Gnanaprakasam} et al., Demonstr. Math. 54, 474--487 (2021; Zbl 07473384) Full Text: DOI References: [1] C. Segre, Le Rappresentazioni Reali delle Forme Complesse a Gli Enti Iperalgebrici, Math. Ann. 40 (1892), 413-467. · JFM 24.0640.01 [2] G. S. Dragoni, Sulle funzioni olomorfe di una variabile bicomplessa, Reale Accad. d’Italia, Mem. Classe Sci. Nat. Fis. Mat. 5 (1934), 597-665. · Zbl 0009.36201 [3] N. Spampinato, Estensione nel campo bicomplesso di due teoremi, del Levi-Civita e del Severi, per le funzioni olomorfe di due variablili bicomplesse I, II, Reale Accad. Naz. Lincei 22 (1935), no. 6, 38-43. · Zbl 0012.26402 [4] N. Spampinato, Sulla rappresentazione delle funzioni do variabile bicomplessa totalmente derivabili, Ann. Mat. Pura Appl. 14 (1936), no. 4, 305-325. · JFM 62.0402.01 [5] H. A. Priestley, Introduction to Complex Analysis, Oxford University Press, Oxford, England, 2008. · Zbl 1127.30002 [6] G. B. Price, An Introduction to Multicomplex Spaces and Functions, Marcel Dekker, New York, 1991. · Zbl 0729.30040 [7] F. Colombo, I. Sabadini, D. C. Struppa, A. Vajiac, and M. Vajiac, Singularities of functions of one and several bicomplex variables, Ark. Math. 49 (2010), 277-294, . · Zbl 1253.30060 · doi:10.1007/s11512-010-0126-0 [8] M. E. Luna-Elizaarrarás, M. Shapiro, D. C. Struppa, and A. Vajiac, Bicomplex numbers and their elementary functions, Cubo 14 (2012), no. 2, 61-80, . · Zbl 1253.30070 · doi:10.4067/S0719-06462012000200004 [9] J. Choi, S. K. Datta, T. Biswas, and N. Islam, Some fixed point theorems in connection with two weakly compatible mappings in bicomplex valued metric spaces, Honam Math. J. 39 (2017), no. 1, 115-126, https://doi.org/10.5831/HMJ.2017.39.1.115. · Zbl 1376.30035 [10] 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. Interdisciplinary Math. 22 (2019), no. 7, 1071-1082, https://doi.org/10.1080/09720502.2019.1709318. [11] S. Choi, S. K. Datta, T. Biswas, and M. Islam, Some fixed point theorems in connection with two weakly compatible mappings in bicomplex valued metric spaces, Honam Math. J. 39 (2017), no. 1, 115-126, https://doi.org/10.5831/HMJ.2017.39.1.115. · Zbl 1376.30035 [12] R. P. Agarwal, S. Gala, and M. A. Ragusa, A regularity criterion in weak spaces to Boussinesq equations, Mathematics 8 (2020), no. 6, 920, 1-14, . · doi:10.3390/math8060920 [13] R. P. Agarwal, O. Bazighifan, and M. A. Ragusa, Nonlinear neutral delay differential equations of fourth-order: Oscillation of solutions, Entropy 23 (2021), no. 2, 129, 1-10, . · doi:10.3390/e23020129 [14] S. K. Datta, D. Pal, N. Biswas, and S. Sarkar, On the study of fixed point theorems in bicomplex valued metric spaces, J. Calcutta Math. Soc. 16 (2020), no. 1, 73-94. [15] I. Beg, S. KumarDatta, and D. Pal, Fixed point in bicomplex valued metric spaces, Int. J. Nonlinear Anal. Appl. 12 (2021), no. 2, 717-727, . · doi:10.22075/ijnaa.2019.19003.2049 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.