Konvergensi Barisan dan Kelengkapan pada Ruang Metrik Parsial Rectangular
Keywords:
convergence sequences, Cauchy sequences, completeness space, rectangular partial metric spaceAbstract
The metric space is one of the objects studied in functional analysis. The metric space has undergone many developments, some eHamples of which are partial metric spaces and rectangular metric spaces. The difference between the metric space and the partial metric space can be seen in the distance of a point from itself. In the metric space, it is always equal to zero, while in the partial metric space it is not equal to zero. On the other hand, the difference between a metric space and a metric rectangular space can be seen in the inequalities used. In the metric space we use triangular inequalities, while in the metric rectangular space we use rectangular inequalities. Shukla in 2014 presents the development of another metric space called rectangular partial metric space, which combines the concept of partial metric space with rectangular metric space. This research we discusses the problem of the properties of the rectangular partial metric space, including convergence sequences, Cauchy sequences, and completeness of space in the rectangular partial metric space.
Downloads
References
E. Kreyszig, Introductory functional analysis with applications. 1976.
O. Kaleva and S. Seikkala, “On fuzzy metric spaces,” Fuzzy Sets Syst, vol. 12, no. 3, pp. 215–229, 1984.
S. Czerwik, “Contraction mappings in b-metric spaces,” 1993.
A. Branciari, “A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces,” 2000.
Y. Zhou, “Fixed point in fuzzy metric spaces,” in Bio-Inspired Computing-Theories and Applications, Springer, 2014, pp. 659–663.
R. I. Sabri, M. RASHEED, O. Alabdali, S. SHIHAB, and T. RASHID, “On Some Properties in Fuzzy Metric Space,” Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13, no. 1, p. Page-55, 2021.
Z. D. Mitrovic, “On an open problem in rectangular b-metric space,” The Journal of Analysis, vol. 25, no. 1, pp. 135–137, 2017.
R. George, S. Radenovic, K. P. Reshma, and S. Shukla, “Rectangular b-metric space and contraction principles,” J. Nonlinear Sci. Appl, vol. 8, no. 6, pp. 1005–1013, 2015.
A. Branciari, “A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces,” 2000.
J. R. Roshan, V. Parvaneh, and Z. Kadelburg, “New fixed point results in b-rectangular metric spaces,” Nonlinear Analysis: Modelling and Control, vol. 21, no. 5, pp. 614–634, 2016.
S. G. Matthews, “Partial Metric Topology,” 1994.
S. Shukla, “Partial rectangular metric spaces and fixed point theorems,” The Scientific World Journal, vol. 2014, 2014, doi: 10.1155/2014/756298.
N. van Dung and V. Thi Le Hang, “A Note on Partial Rectangular Metric Spaces,” 2014.
