Weakly Contractive Mapping and Weakly Kannan Mapping in Partial Metric Space

  • S. Sunarsini Departemen Matematika, Fakultas Matematika Komputasi dan Sains Data, Institut Teknologi Sepuluh Nopember Surabaya
  • S. Sadjidon Departemen Matematika, Fakultas Matematika Komputasi dan Sains Data, Institut Teknologi Sepuluh Nopember Surabaya
  • Annisa Rahmita Departemen Matematika, Fakultas Matematika Komputasi dan Sains Data, Institut Teknologi Sepuluh Nopember Surabaya

Abstract

In the article the concept of metric space could be expanded, one of which is a partial metric space. In the metric space, the distance of a point to itself is equal to zero, while in the partial metric space need not be equal to zero.The concept of partial metric space is used to modify Banach's contraction principle. In this paper, we discuss weakly contractive mapping and weakly Kannan mapping which are extensions of Banach's contraction principle to partial metric space together some related examples. Additionally, we discuss someLemmas which are shows an analogy between Cauchy sequences in partial metric space with Cauchy sequences in metric space and analogy between the complete metric space and the complete partial metric space.
Keywords: Cellulose metric space, partial metric space, weakly contraction mapping, weakly Kannan mapping.

References

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Alghamdi, Maryam A, Naseer S, Oscar V. 2012. On Fixed Point Theory in Partial Metric Spaces.Fixed Point Theory and Applications. 175:1-25.

Dugundji, J dan A. Granas. 1978.Weakly Contractive Maps and Elementary Domain Invariance Theorem*. Bull. Greek Math. Soc. 19: 141-151.

Kannan, R. 1968. Some Results On Fixed Points. Bulletin of the Calcutta Mathematical Society. 60:71-76.

Kreyszig, E. 1978. Introductory Functional Analysis with Aplication. Canada: John Wiley and Sons, Inc.Canada.

Matthews, SG. 1994. Partial Metric Topology. Annals of the New York Academy of Sciences, 183 - 197.
Published
2019-01-22
How to Cite
SUNARSINI, S.; SADJIDON, S.; RAHMITA, Annisa. Weakly Contractive Mapping and Weakly Kannan Mapping in Partial Metric Space. Jurnal ILMU DASAR, [S.l.], v. 20, n. 1, p. 33-38, jan. 2019. ISSN 2442-5613. Available at: <https://jurnal.unej.ac.id/index.php/JID/article/view/6782>. Date accessed: 16 july 2019. doi: https://doi.org/10.19184/jid.v20i1.6782.
Section
General