Fixed Point and Coincidence Point Theorems in Dualistic Partial Metric Spaces
Manoj Ughade
Department of Mathematics, Institute for Excellence in Higher Education (IEHE), Bhopal-462016, Madhya Pradesh, India.
Sheetal Yadav *
Department of Mathematics, Mata Gujri Mahila Mahavidhyala (Auto), Jabalpur-482001, Madhya Pradesh, India.
Rahul Gourh
Department of Mathematics, Govt LBS PG College, Sironj, Vidisha, Madhya Pradesh, 464228, India.
Manoj Kumar Shukla
Department of Mathematics, Institute for Excellence in Higher Education (IEHE), Bhopal-462016, Madhya Pradesh, India.
*Author to whom correspondence should be addressed.
Abstract
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\(\Delta\) -contraction, generalized dualistic E\(\Delta\)-contraction, and Dass-Gupta dualistic rational E\(\Delta\) -contraction. We establish some common fixed-point theorems for E\(\Delta\) -contraction, generalized dualistic E\(\Delta\)-contraction and Dass-Gupta dualistic rational E\(\Delta\)-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.
Keywords: Fixed point theorem, DPM space, E-contraction, rational E-contraction