A new type of fixed point theorem in metric spaces

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Various Suzuki type theorems in b -metric spaces (2015, result): “Now, we are ready to prove the following Suzuki type theorems for nonlinear contractions.”
Fixed Point Results for F-Contractive Mappings of Hardy-Rogers-Type (2014, background): “Starting from these considerations, the study of fixed and common fixed points of mappings satisfying a certain metrical contractive condition attracted many researchers, see for example [1–3, 5, 6, 8–11, 16, 22–27].”
F-contractions of Hardy–Rogers-type and application to multistage decision (2016, background): “Moreover, T is said an F -contraction of Suzuki–Hardy–Rogers type if (2) holds for all x, y ∈ X with Tx 6= Ty and d(x, Tx)/2 < d(x, y), see also [8, 25].”
Multi-valued F-contractions and the solutions of certain functional and integral equations (2013, background): “Starting from these considerations, the study of fixed and common fixed points of mappings satisfying a certain metrical contractive condition attracted many researchers, see for example [3, 4, 6, 11, 14, 15, 21, 23–28].”
Some fixed point generalizations are not real generalizations (2011, unknown): “The following result of Suzuki [8] generalizes the well-known fixed point theorem due to Edelstein [9].”