Ample Spectrum Contractions and Related Fixed Point Theorems
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R-functionSimulation functionManageable functionFixed pointContractivity conditionBinary relation
Roldán López de Hierro, A. F., & Shahzad, N. (2019). Ample Spectrum Contractions and Related Fixed Point Theorems. Mathematics, 7(11), 1033.
SponsorshipThis article was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah.
Simulation functions were introduced by Khojasteh et al. as a method to extend several classes of fixed point theorems by a simple condition. After that, many researchers have amplified the knowledge of such kind of contractions in several ways. R-functions, (R, S)-contractions and (A, S)-contractions can be considered as approaches in this direction. A common characteristic of the previous kind of contractive maps is the fact that they are defined by a strict inequality. In this manuscript, we show the advantages of replacing such inequality with a weaker one, involving a family of more general auxiliary functions. As a consequence of our study, we show that not only the above-commented contractions are particular cases, but also another classes of contractive maps correspond to this new point of view.