Characterizations of partial metric completeness in terms of weakly contractive mappings having fixed point

Abstract

We characterize both complete and 0-complete partial metric spaces in terms of weakly contractive mappings having a fixed point. Our results extend a well-known characterization of metric completeness due to Suzuki and Takahashi to the partial metric framework.

Existence of common fixed points of improved F-contraction on partial metric spaces

“…In fact, a partial metric space is a generalization of metric space in which the self distances p(r 1 , r 1 ) of elements of a space may not be zero and follows the inequality p(r 1 , r 1 ) ≤ p(r 1 , r 2 ). After this remarkable contribution, many authors took interest in partial metric spaces and its topological properties and presented several well known fixed point results in the framework of partial metric spaces (see [1,2,3,4,12] and references therein). In 1922, Banach presented a landmark fixed point result (Banach Contraction Principle).…”

Generalized Geraghty type mappings on partial metric spaces and fixed point results

“…Later on, Abdeljawad et al [1], Acar et al [2,3], Altun et al [4][5][6][7], Karapinar and Erhan [15], Oltra and Valero [17] and Valero [23] gave some generalizations of the result of Matthews. Also,Ćirić et al [8], Samet et al [21] and Shatanawi et al [22] proved some common fixed point results in partial metric spaces.…”

Weak condition for generalized f-weakly Picard mappings on partial metric spaces

“…Afterward, Acar et al [1,2], Altun et al [4,5,7,8], Karapinar and Erhan [17], Oltra and Valero [21], Romaguera [22,23] and Valero [31], gave some generalizations of the result of Matthews. Also, Ciric et al [13], Samet et al [27] and Shatanawi et al [30] proved some common fixed point results in partial metric spaces.…”