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JP Journal of Fixed Point Theory and Applications

JP Journal of Fixed Point Theory and Applications
Volume 3, Issue 2, Pages 123 - 132 (August 2008)

FIXED-POINT THEOREMS FOR SOME ORDER-CONTRACTIVE MAPPINGS Yuqiang Feng (P. R. China) Received December 3, 2007 References:
[1] H. Amann, On the number of solutions of nonlinear equations in ordered Banach spaces, J. Funct. Anal. 11 (1972), 346-384. [2] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985. [3] J. J. Nieto and R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005), 223-239. [4] J. J. Nieto, Rodrigo L. Pouso and R. Rodríguez-López, Fixed point theorems in ordered abstract spaces, Proc. Amer. Math. Soc. 135 (2007), 2505-2517. [5] A. Petruşel and I. A. Rus, Fixed point theorems in ordered L-space, Proc. Amer. Math. Soc. 134 (2006), 411-418. [6] André C. M. Ran and Martine C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004), 1435-1443. [7] Fang Shuhong, Semilattice structure of fixed point set for increasing operators, Nonliear Anal. (TMA) 27 (1996), 793-796. [8] Zhang Xian, Fixed point of ordered contractive maps, Acta Math. Sinica 48 (2005), 973-978.

Keywords and phrases: order-contractive mappings, fixed-point theorem, existence, uniqueness.

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