Fixed Point and Coincidence Point Theorems in Dualistic Partial Metric Spaces

In this paper, motivated by Fulga and Proca [1], we define the notion of dualistic E-contraction, generalized dualistic E-contraction, and Dass-Gupta dualistic rational E-contraction. We establish some new fixed-point theorems for E-contraction, generalized dualistic E-contraction, and Dass-Gupta dualistic rational E-contraction in a DPM space. Also, we define dualistic E∆-contraction, generalized dualistic E∆-contraction, and Dass-Gupta dualistic rational E∆-contraction. We establish some common fixed-point theorems for E∆-contraction, generalized dualistic E∆-contraction and Dass-Gupta dualistic rational E∆-contraction in the setting of DPM spaces. Our results extend and generalize some well-known results of [1] and [2]. We also provide an example that shows the usefulness of these contractions.