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The aim of our paper is to present a new class of functions and to define some new contractive mappings in b-metric spaces. We establish some fixed point results for these new contractive mappings in b-metric spaces. Furthermore, we extend our main result in the framework of b-metric-like spaces. Some consequences of main results are also deduced. We present some examples to illustrate and support our results. We provide an application to solve simultaneous linear equations. In addition, we present some open problems.

Some Fixed Point Results in b-Metric Spaces and b-Metric-Like Spaces with New Contractive Mappings