@article{Nazir2023, 
author = {Talat Nazir and Zakaria Ali and Shahin Nosrat Jogan and Manuel de la Sen},
title = {On a class of fixed points for set contractions on partial metric spaces with a digraph},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {1},
pages = {1304-1328},
keywords = {fixed point, set-contraction, partial metric space, graph, graph contraction},
url = {https://www.sciopen.com/article/10.3934/math.2023065},
doi = {10.3934/math.2023065},
abstract = {We investigate the existence of fixed point problems on a partial metric space. The results obtained are for set contractions in the domain of sets and the pattern for the partial metric space is constructed on a directed graph. Essentially, our main strategy is to employ generalized    ϕ-contractions in order to prove our results, where the fixed points are investigated with a graph structure. Moreover, we state and prove the well-posedness of fixed point based problems of the generalized    ϕ-contractive operator in the framework of a partial metric space. We illustrate the main results in this manuscript by providing several examples.}
}