Some new results on fixed and best proximity points in preordered metric spaces

Abstract

In this paper, we first introduce two new classes of (ω,δ)- contractions of the first and second kinds and establish some related new fixed point and best proximity point theorems in preordered metric spaces. Our theorems subsume the corresponding recent results of Samet (J. Optim. Theory Appl. (2013), doi:10.1007/s10957-013-0269-9) and extend and generalize many of the well-known results in the literature. An example is also provided to support our main results. ©2013 Amini-Harandi et al.; licensee Springer.