Abstract:
Based on a class of semicontinuous functions, we prove a common fixed point theorem for a pair of commuting mappings. As a consequence, we give another common fixed point for the so-called weakly contractive mappings of type $E_T$. The proven results are established in the setting of bounded metric spaces without using neither the compactness nor the uniform convexity. Some examples are built to demonstrate the superiority of the obtained results compared to the existing ones in the literature. Furthermore, an application to a system of functional equations arising in dynamic programming is given.
Keywords:сommon fixed point, weakly contractive maps of type $E_T$, commuting maps, compactness, uniform convexity.
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