PARTIAL CONE METRIC SPACE AND SOME FIXED POINT THEOREMS

Yıl 2013, Cilt: 3 Sayı: 1, 1 - 9, 01.06.2013

D. Dey M. Saha

Öz

In the present paper, we have proved some convergence properties of a sequence of elements in a partial cone metric space and thereby we have established some fixed point theorems on it.

Anahtar Kelimeler

Partial metric space, partial cone metric space, Şxed point

Kaynakça

• [1] Banach, S., (1922), Sur les operations dans les ensembles abstraits et leur application aux quations intgrales, Fund. Math., 3 ,133-181 (French).
• [2] Chatterjee, S. K., (1972), Fixed point theorems, Rend. Acad. Bulgare Sc., 25, 727-730.
• [3] Huang, L.-G. and Zhang, X., (2007), Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332(2), 1468-1476.
• [4] Kannan, R., (1968), Some results on fixed points, Bull. Calcutta Math. Soc., 60, 71-76.
• [5] K¨unzi, H.P.A., (Dordrecht, 2001), Nonsymmetric distances and their associated topologies: About the origins of basic ideas in the area of asymmetric topology, Handbook of the History of General Topology (eds. C.E. Aull and R. Lowen), Kluwer Acad. Publ., 3, 853-968.
• [6] Lin, S.D., (1987), A common fixed point theorem in abstract spaces, Indian Journal of Pure and Applied Mathematics, 18(8), 685-690.
• [7] Matthews, S., (1994), Partial Metric Topology, Proceedings of the 8th Summer Conference on Topology and its Applications, Annals of The New york Academy of Sciences, 728, 183-197.
• [8] Bukatin, M., Kopperman, R., Matthews, S. and Pajoohesh, H., (october, 2009), Partial Metric Spaces, The Mathematical Association of America, 116, 708-718.
• [9] Reich, S., (1971), Kannan’s fixed point thorem, Boll. Un. Math. Ital., 4, 1-11.
• [10] Romaguera, S. and Schellekens, M., (2003), Weightable quasi-metric semigroups and semilattices, Proc. MFCSIT2000, Electronic Notes in Theoretical Computer Science, 40, 12 pages.
• [11] Rzepecki, B., (1980), On fixed point theorems of Maia type, Publications de lInstitut Mathematique, 28(42), 179-186.
• [12] S¨onmez, A., (14 Jan, 2011), Fixed point theorems in partial cone metric spaces, arXiv:1101.2741v1 [math.GN].
• [13] Valero, O., (2005), On Banach fixed point theorems for partial metric spaces, Appl. Gen. Top, 6(2), 229-240.