Ample Spectrum Contractions and Related Fixed Point Theorems
Metadatos
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MDPI
Materia
R-function Simulation function Manageable function Fixed point Contractivity condition Binary relation
Fecha
2019-11-02Referencia bibliográfica
Roldán López de Hierro, A. F., & Shahzad, N. (2019). Ample Spectrum Contractions and Related Fixed Point Theorems. Mathematics, 7(11), 1033.
Patrocinador
This article was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah.Resumen
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.