Some properties of T-metric spaces and a common fixed point theorem

• Autorzy: Sedghi S. , Altun I. , Shobe N.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduce the new definitions of T-metric space and give some properties of it. Also, we prove a common fixed point theorem for for four mappings under the condition of weakly compatible in complete T-metric spaces. A lot of fixed point theorems on ordinary metric space are special case of our main result, since every ordinary metric space is also T-metric space.

Słowa kluczowe

EN

T-metric space; contractive mapping; fixed point

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2012
• Tom: Nr 48
• Strony: 105--118
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Sedghi S.

• Department of Mathematics Islamic Azad University Qaemshahr Branch, Qaemshahr, P.O.Box 163, Iran

autor

Altun I.

• Department of Mathematics Faculty of Science and Arts Kirikkale University 71450 Yahsihan, Kirikkale, Turkey

autor

Shobe N.

• Department of Mathematics Islamic Azad University Science and Research Branch 14778 93855 Tehran, Iran

Bibliografia

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• [3] Altun I., Turkoglu D., Some fixed point theorems for weakly compatible mappings satisfying an implicit relation, Taiwanese J. Math., 13(4)(2009), 1291-1304.
• [4] Berinde V., Iterative Approximation of Fixed Points, Springer, 2007.
• [5] Ciric Lj.B., Fixed Point Theory, Contraction Mapping Principle, Faculty of Mechanical Engineering, Beograd, 2003.
• [6] Granas A., Dugundji J., Fixed Point Theory, Springer, 2010.
• [7] Imdad M., Kumar S., Khan M.S., Remarks on some fixed point theorems satisfying implicit relation, Rad. Math., 11(2002), 135-143.
• [8] Jungck G., Rhoades B.E., Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math., 29(3)(1998), 227-238.
• [9] Mihet D., A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems, 144(3)(2004), 431-439.
• [10] Popa V., Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math., 32(1)(1999), 157-163.
• [11] Rao K.P.R., Kishore G.N.V., Common fixed point theorems in ultra metric spaces, Punjab University Journal of Mathematics, 40(2008), 31-35.
• [12] Sedghi S., Altun I., Shobe N., A fixed point theorem for multi-maps satisfying an implicit relation on metric spaces, Appl. Anal. Discrete Math., 2(2)(2008), 189-196.
• [13] Turkoglu D., Fixed point theorems on uniform spaces, Indian J. Pure Appl. Math., 34(3)(2003), 453-459.
• [14] Rooyij A.C.M.V., Non-Archimedean Functional Analysis, Marcel Dekker, New York, 1978.