Fixed Point Theorems in Partial Metric Spaces

Abstract

In this chapter, we recollect some crucial and exciting fixed point theorems in the context of partial metric space. In addition, we underline the importance of the partial metric space in fixed point theory. Matthews [210] not only introduced the partial metric spaces but also obtained the first fixed point theorem in this new setting. More precisely, Matthews [210] showed that the famous Banach fixed point theory is valid in the framework of complete partial metric space. After this pioneering result of Matthews [210] in fixed point theory, a considerable number of researchers have investigated the partial metric spaces, and remarkable number of fixed point results in the context of partial metrics have appeared in the literature (see e.g. [1, 2, 7, 27–30, 34, 38–40, 42, 46, 49–53, 86, 92, 94, 102, 120, 125, 130, 136, 137, 146, 154, 155, 157, 164–166, 173, 175, 176, 178, 181, 188, 189, 202, 204, 210, 211, 222, 225, 230, 243, 245–250, 255, 258, 261, 262, 265, 266, 272–278] and the reference therein). © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.