ORDERED-THEORETIC FIXED POINT RESULTS FOR MONOTONE GENERALIZED BOYD-WONG AND MATKOWSKI TYPE CONTRACTIONS

In the setting of partially ordered metric spaces, we prove some fixed point theorems for monotone generalized and lean generalized ϕ-contractions wherein the utilized control function is either of Boyd-Wong or Matkowski type. Our main results generalize several known results of the existing literature especially those contained in Agarwal et al. (2008), Ciric et al. (2008), Nieto and Rodrıguez-Lopez (2005, 2007), Ran and Reurings (2004) and Wu and Liu (2013). We furnish several examples to illustrate the usability of our results especially one of these examples disprove Remark in Agarwal et al. (2008). Some applications are also discussed.