Fixed points and common fixed points theorems in pseudo-ordered sets
DOI:
https://doi.org/10.4067/S0716-09172013000400008Keywords:
Pseudo-ordered set, Fixed point, Monotone map, Complete trellis.Abstract
Under suitable conditions, we establish the existence of the greatest and the least fixed points of monotone maps defined on nonempty pseudo-ordered sets. Also, we prove that the set of all common fixed points of two categories of finite commutative family F of monotone maps f defined on a nonempty complete trellis is also a nonempty complete trellis.References
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[2] Altun I., Simsek H.: Some fixed point theorems on ordered metric spaces and application. Fixed Point Theory Appl 2010 ; 2010. Article ID 621469, 17 pages, doi:10.1155/2010/621469.
[3] Amann, H., Order structures and fixed points, Ruhr-universitat, Bochum, mimeographed lecture notes, (1977).
[4] Hemant Kumar Nashine, Bessem Samet and Calogero Vetro (2012): Fixed Point Theorems in Partially Ordered Metric Spaces and Existence Results for Integral Equations, Numerical Functional Analysis and Optimization, 33:11, pp. 1304-1320.
[5] Knaster, B.: un théorème sur les fonctions d’ensembles, Annales de la Societé Polonaise de Mathématique vol. 6, pp. 133-134, (1968).
[6] Nieto, J. J. and Rodríguez-Lopez, R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, vol. 22, no. 3, pp. 223239, (2005).
[7] Nieto, J. J. and Rodríguez-Lopez, R.: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Mathematica Sinica, vol. 23, no. 12, pp. 22052212, (2007).
[8] Parameshwara Bhatta, S., Shashirekha, H.: A characterisation of completeness for Trellises. Algebra univeralis 44, pp. 305-308, (2000).
[9] Parameshwara Bhatta, S.: Weak chain completeness and fixed point property for pseudo-ordered sets. Czechoslovac Mathematical Journal 55 (130), pp. 365-369, (2005).
[10] Skala, H. L.: Trellis theory. Algebra Universalis 1, pp. 218-233, (1971).
[11] Skala, H. L.: Trellis theory. Mem. Amer. Math. Soc. 121, Providence, (1972).
[12] Stouti, A. : A generalized Amman fixed point theorem and its applications to Nash equilibrium, Acta Academiae Paedagogicae Ny’iregyh’aziensis, 21, no. 2, pp. 107-112, (2005).
[13] Tarski, A.: A Lattice-Theoretical Fixpoint Theorem and its Applications Pacific J. Math, pp. 285-309 5(1955).
[14] Ran, A. C. M. and Reurings, M. C. B.: A fixed point theorem in partially ordered sets and some applications to matrix equations, Proceedings of the American Mathematical Society, vol. 132, no. 5, pp. 14351443, (2004).
[15] E. Zeidler: Nonlinear Functional Analysis and its Applications, I. Fixed-Point Theorems, Springer-Verlag, New-York, (1986).
How to Cite
[1]
A. Stouti and A. Maaden, “Fixed points and common fixed points theorems in pseudo-ordered sets”, Proyecciones (Antofagasta, On line), vol. 32, no. 4, pp. 409-418, 1.
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