In this work, we extend and complement some results in the field of fixed point theory in view of general and wider structures, such as b-spaces (respectively b-metric and b-metric-like spaces). Considering existing classes of Z- contractions and Ψ- simulating functions with a solid impact in database results of fixed point theory (can see [1]-[3], [8]-[16], [18]-[21]), we introduce a new general class of simulating functions called as Ψ- s simulation functions, and also types of K_(Ψ-s) - contractions in a more general framework. This approach covers, extends and unifies several work considered in the existing literature.
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