Warianty tytułu
Języki publikacji
Abstrakty
The convergence of sequences and non-unique fixed points are established in ℳ-orbitally complete cone metric spaces over the strongly minihedral cone, and scalar weighted cone assuming the cone to be strongly minihedral. Appropriate examples and applications validate the established theory. Further, we provide one more answer to the question of the existence of the contractive condition in Cone metric spaces so that the fixed point is at the point of discontinuity of a map. Also, we provide a negative answer to a natural question of whether the contractive conditions in the obtained results can be replaced by its metric versions.(original abstract)
Słowa kluczowe
Twórcy
autor
- Government Degree College Thatyur (Tehri Garhwal) Uttarakhand India
autor
- S.G.R.R. (P.G.) College Dehradun India
Bibliografia
- Aliprantis C.D. and Tourky R., Cones and Duality, Graduate Studies in Mathematics, 84, American Mathematical Society, Providence, 2007.
- Deimling K., Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.
- Huang L.G. and Zhang X., Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), no. 2, 1468-1476.
- Kadelburg Z., Radenović S., and Rakočević V., Topological vector space-valued cone metric spaces and fixed point theorems, Fixed Point Theory Appl. 2010, Art. ID 170253, 17 pp.
- Kantorovich L.V., On some further applications of the Newton approximation method, Vestnik Leningrad. Univ. Ser. Mat. Meh. Astr. 12 (1957), no. 7, 68-103 (in Russian).
- Karapınar E., Some nonunique fixed point theorems of Ćirić type on cone metric spaces, Abstr. Appl. Anal. 2010, Art. ID 123094, 14 pp.
- Khamsi M.A., Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl. 2010, Art. ID 315398, 7 pp.
- Lin S.D., A common fixed point theorem in abstract spaces, Indian J. Pure Appl. Math. 18 (1987), no. 8, 685-690.
- Rezapour Sh. and Hamlbarani R., Some notes on the paper "Cone metric spaces and fixed point theorems of contractive mapping", J. Math. Anal. Appl. 345 (2008), no. 2, 719-724.
- Rhoades, B.E. Contractive definitions and continuity, in: R.F. Brown (ed.), Fixed Point Theory and Its Applications, Contemp. Math., 72, Amer. Math. Soc., Providence, 1988, pp. 233-245.
- Rzepecki B., On fixed point theorems of Maia type, Publ. Inst. Math. (Beograd) (N.S.) 28(42) (1980), 179-186.
- Sonmez A. and Cakalli H., Cone normed spaces and weighted means, Math. Comput. Modelling 52 (2010), no. 9-10, 1660-1666.
- Vandergraft J.S., Newton's method for convex operators in partially ordered spaces, SIAM J. Numer. Anal. 4 (1967), 406-432.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171629194