# MONOTONE GENERALIZED CONTRACTIONS IN ORDERED METRIC SPACES

• Alam, Aftab (Department of Mathematics Aligarh Muslim University) ;
• Imdad, Mohammad (Department of Mathematics Aligarh Muslim University)
• Received : 2014.12.11
• Published : 2016.01.31
• 99 8

#### 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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