Fixed point theory in partial metric spaces via φ-fixed point’s concept in metric spaces

Abstract

Let X be a non-empty set. We say that an element [InlineEquation not available: see fulltext.] is a φ-fixed point of T, where [InlineEquation not available: see fulltext.] and [InlineEquation not available: see fulltext.], if x is a fixed point of T and [InlineEquation not available: see fulltext.]. In this paper, we establish some existence results of φ-fixed points for various classes of operators in the case, where X is endowed with a metric d. The obtained results are used to deduce some fixed point theorems in the case where X is endowed with a partial metric p. MSC:54H25, 47H10.