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A $phi$ - contraction Principle in Partial Metric Spaces with Self-distance Terms | | Thabet Abdeljawad
; Younis Zaidan
; Naseer Shahzad
; | | Date: |
2 Oct 2012 | | Abstract: | We prove a generalized contraction principle with control function in
complete partial metric spaces. The contractive type condition used allows the
appearance of self distance terms. The obtained result generalizes some
previously obtained results such as the very recent " D. Ili’{c}, V.
Pavlovi’{c} and V. Rakou{c}evi’{c}, Some new extensions of Banach’s
contraction principle to partial metric spaces, Appl. Math. Lett. 24 (2011),
1326--1330". An example is given to illustrate the generalization and its
properness. Our presented example does not verify the contractive type
conditions of the main results proved recently by S. Romaguera in " Fixed point
theorems for generalized contractions on partial metric spaces, Topology Appl.
159 (2012), 194-199" and by I. Altun, F. Sola and H. Simsek in "Generalized
contractions on partial metric spaces, Topology and Its Applications 157 (18)
(2010), 2778--2785". Therefore, our results have an advantage over the
previously obtained. | | Source: | arXiv, 1210.0671 | | Services: | Forum | Review | PDF | Favorites | |
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