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http://dx.doi.org/10.4134/BKMS.2016.53.1.061

MONOTONE GENERALIZED CONTRACTIONS IN ORDERED METRIC SPACES  

Alam, Aftab (Department of Mathematics Aligarh Muslim University)
Imdad, Mohammad (Department of Mathematics Aligarh Muslim University)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.1, 2016 , pp. 61-81 More about this Journal
Abstract
In this paper, we prove some existence and uniqueness results on coincidence points for g-monotone mappings satisfying linear as well as generalized nonlinear contractivity conditions in ordered metric spaces. Our results generalize and extend two classical and well known results due to Ran and Reurings (Proc. Amer. Math. Soc. 132 (2004), no. 5, 1435-1443) and Nieto and $Rodr{\acute{i}}guez$-$L{\acute{o}}pez$ (Acta Math. Sin. 23 (2007), no. 12, 2205-2212) besides similar other ones. Finally, as an application of one of our newly proved results, we establish the existence and uniqueness of solution of a first order periodic boundary value problem.
Keywords
ordered metric space; TCC property; termwise monotone sequence; c-bound;
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