Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 2026 01 06 Existence of fixed point for generalized weak contraction satisfying rational type expression in partially ordered metric spaces 10420 10.22075/ijnaa.2025.28350.3865 EN Joginder Paul Department of Mathematics, H.N.B. Garhwal University, B.G.R. Campus, Pauri-246001, Uttarakhand, India U.C. Gairola Department of Mathematics, H.N.B. Garhwal University, B.G.R. Campus, Pauri-246001, Uttarakhand, India Journal Article 2022 09 09 In this paper, we obtain some fixed point theorems of mappings satisfying a generalized rational type weak contractive condition in partially ordered metric spaces. The presented results generalize and extend various fixed point theorems of the literature. We also provide an example which supports our new results, but it contradicts the previously established results. Furthermore, we discuss the application of these results to the existence and uniqueness of solutions for first-order periodic boundary value problems arising in ordinary differential equations. https://ijnaa.semnan.ac.ir/article_10420_ca751e6ab38280edada823df9cb45a93.pdf