In the literature one can find some interesting papers concerning cyclic contraction, F-contraction and weakly compatible mapping (see for example [17 26]).
Recently, Wardowski [7] introduced a new type of contraction called F-contraction in his studies of contractive maps and proved a new fixed point theorem concerning F-contractions, for which the Banach contraction principle and some other known contractive conditions in the literature can be obtained as special cases.
In fact 0 is the unique fixed point of T. In 1974, Ciric [3] introduced the concept of a quasi-contraction and extended some results concerning generalized contractions of [43] and [44] to quasi-contractions.
The muscle spindles send information to the nervous system concerning muscle contraction speed, through large sensory fibres, and related to muscle length, through smaller sensory fibres.
Following this direction of research, we introduce the new concepts of an α-type almost-F-contraction and an α-type F-Suzuki contraction and prove some fixed point theorems concerning such contractions.
In the present article, using a mapping F: ℝ+ → ℝ we introduce a new type of contraction called F-contraction and prove a new fixed point theorem concerning F-contraction.
In 2012, Wardowski [11] introduce a new type of contractions called F-contraction and prove a new fixed point theorem concerning F-contractions.
In this regard, starting from a function F : ( 0, ∞ ) → R satisfying some suitable properties, Wardowski provided in [11] a new type of such a contractive mapping, namely F-contraction, and proved a fixed point theorem concerning F-contractions on a complete metric space.
So if keeping a record of the "informational cost" of the execution of some information processing is a concern, Contraction will be rejected.
In the literature one can find some interesting papers concerning F-contractions; e.g., in [2] the authors investigated F-contractions of Hardy-Rogers type.
