Almost Contractions under Binary Relations

Abstract

After the introduction of almost contraction due to Berinde, the branch of metric fixed point theory has attracted much attention in this direction, and various fixed point results have been proved for almost contractions via different approaches. In this paper, the results on existence and uniqueness of fixed points are proved employing almost contraction conditions in the framework of metric space endowed with binary relation. Finally, some examples are constructed, which substantiate the utility of the newly proved results.

Keywords

• almost contractions
• <i>ϱ</i>-self-closedness
• ℱ-closedness