Common Fixed Point Theorems for Weakly $(\psi,S,C)$-Contractive Mappings in Partially Ordered $b$-Metric Spaces

Le Thi Chac, Nguyen Trung Hieu

Abstract

In this paper, we introduce the notions of  weakly $(\psi,S,C)$-contractive mappings and generalized weakly $(\psi,S,C)$-contractive mappings in partially ordered $b$-metric spaces and state some common fixed point theorems for these classes of mappings. These results generalize and improve the main results in [H.K. Nashine, Common fixed points via weakly $(\psi, S, C)$-contraction mappings on ordered metric spaces and application to integral equations, Thai J. Math. 12 (3) (2014) 729--747]. Also, some examples are given to illustrate the~results.