Abstract
References
- C. D. Aliprantis, K. C. Border, Infinite Dimensional Analysis, Springer-Verlag, Berlin, 1999.
- I. Altun, C. Çevik, Some common fixed point theorems in vector metric spaces, Filomat, 25(1), (2011), 105-113.
- C. Çevik, I. Altun, Vector metric spaces and some properties, Topol. Methods Nonlinear Anal., 34(2) (2009), 375-382.
- C. Çevik, On continuity of functions between vector metric spaces, J. Funct. Spaces, (2014) Article ID 753969, 6 pages.
- F. Dashiell, A. Hager, M. Henriksen, Order-Cauchy completions of rings and vector lattices of continuous functions, Can. J. Math. (3) 32 (1980), 657-685.
- C. J. Everett, Sequence completion of lattice moduls, Duke Math. J. 11 (1944), 109-119.
- J.L. Krivine, Theoremes de factorisation dans les espaces reticules, Seminaire Maurey-Schwartz (1973- 74), Exposes 22-23, École Polytechnique, Paris.
- Y. Lindenstrauss, L. Tzafriri, Classical Banach Spaces II, Springer-Verlag, Berlin-Heidelberg-New York, 1979.
- W. A. J. Luxemburg, A. C. Zaanen, Riesz Space I, North-Holland, Amsterdam, 1971.
- Zs. Páles, I.-R. Petre, Iterative fixed point theorems in E-metric spaces, Acta Math. Hungar., 140(1-2), (2013) 134-144.
- F. Papangelou, Order convergence and topological completion of commutative lattice-groups, Math. Annalen 155 (1964), 81-107.
- I.-R. Petre, Fixed point theorems in vector metric spaces for single-valued operators, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity, 9 (2011), 59-80.
- I.-R. Petre, Fixed points for ϕ-contractions in E- Banach spaces, Fixed Point Theory, 13(2), (2012), 623- 640.
- V. Zaharov, On functions connected with sequential absolute, Cantor completions and classical rings of quotients, Periodica Math. Hungar. 19 (1988), 113-133.
Abstract
In this study a completion theorem for vector metric spaces is proved. The completion spaces are defined by means of an equivalence relation obtained by order convergence via the module of the Riesz space E.
Keywords
Vector metric space order-Cauchy sequence order-Cauchy completion Riesz space Banach lattice
References
- C. D. Aliprantis, K. C. Border, Infinite Dimensional Analysis, Springer-Verlag, Berlin, 1999.
- I. Altun, C. Çevik, Some common fixed point theorems in vector metric spaces, Filomat, 25(1), (2011), 105-113.
- C. Çevik, I. Altun, Vector metric spaces and some properties, Topol. Methods Nonlinear Anal., 34(2) (2009), 375-382.
- C. Çevik, On continuity of functions between vector metric spaces, J. Funct. Spaces, (2014) Article ID 753969, 6 pages.
- F. Dashiell, A. Hager, M. Henriksen, Order-Cauchy completions of rings and vector lattices of continuous functions, Can. J. Math. (3) 32 (1980), 657-685.
- C. J. Everett, Sequence completion of lattice moduls, Duke Math. J. 11 (1944), 109-119.
- J.L. Krivine, Theoremes de factorisation dans les espaces reticules, Seminaire Maurey-Schwartz (1973- 74), Exposes 22-23, École Polytechnique, Paris.
- Y. Lindenstrauss, L. Tzafriri, Classical Banach Spaces II, Springer-Verlag, Berlin-Heidelberg-New York, 1979.
- W. A. J. Luxemburg, A. C. Zaanen, Riesz Space I, North-Holland, Amsterdam, 1971.
- Zs. Páles, I.-R. Petre, Iterative fixed point theorems in E-metric spaces, Acta Math. Hungar., 140(1-2), (2013) 134-144.
- F. Papangelou, Order convergence and topological completion of commutative lattice-groups, Math. Annalen 155 (1964), 81-107.
- I.-R. Petre, Fixed point theorems in vector metric spaces for single-valued operators, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity, 9 (2011), 59-80.
- I.-R. Petre, Fixed points for ϕ-contractions in E- Banach spaces, Fixed Point Theory, 13(2), (2012), 623- 640.
- V. Zaharov, On functions connected with sequential absolute, Cantor completions and classical rings of quotients, Periodica Math. Hungar. 19 (1988), 113-133.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | February 23, 2015 |
| Published in Issue | Year 2015 Volume: 28 Issue: 1 |