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\(Δ\) -contraction, generalized dualistic E\(Δ\)-contraction, and Dass-Gupta dualistic rational E\(Δ\) -contraction. We establish some common fixed-point theorems for E\(Δ\) -contraction, generalized dualistic E\(Δ\)-contraction and Dass-Gupta dualistic rational E\(Δ\)-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.