摘要：In this paper, we introduce the concept of a generalized weak ( ϕ , R ) $(\phi,\mathcal{R})$ -contraction and employ this to prove some fixed point results for self-mappings in partial metric spaces endowed with a binary relation R $\mathcal{R}$ . We also establish some consequences in ordered partial metric spaces and metric spaces with a binary relation and exemplify that our results are a sharpened version of results of Zhiqun Xue (Nonlinear Funct. Anal. Appl. 21(3):497–500, 2016) and Alam and Imdad (J. Fixed Point Theory Appl. 17(4):693–702, 2015). Finally, we provide the existence of a solution for integral and fuzzy partial differential equations.
关键词：Partial metric space ; Binary relation ; Preserving mappings ; \(\mathcal{R}^{\neq}\) -precompleteness ; \(\mathcal{R}^{\neq}\) -continuous ; Partial order
