During muscle contraction, for which the primary function of β-oxidation is the provision of energy, the β-oxidation flux is regulated through the ATP levels and the ratio of NAD+ to NADH [ 52, 53].
In particular, we give an example of a nonlinear contraction mapping for which our result successfully detects a coupled fixed point in contrast to the result of Sintunavarat et al., which is not applied to show the existence of a coupled fixed point.
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.
He introduced the notion of single-valued G-contraction for which he obtained fixed point results.
They introduced the notions of multivalued G-contractions and weak G-contractions for which they established fixed point theorems.
In Section 4, we introduce the class of multivalued weak G-contractions, for which we study the existence of fixed points.
"Indeed, with the fading of the Olympic boost likely to weigh on GDP in the fourth quarter, the [Bank of England's] monetary policy committee has said that it is braced for a contraction – which is what we expect.
Let ( X, d ) be a complete metric space and T : X → X be an almost contraction, that is, a mapping for which there exist a constant k ∈ [ 0, 1 ) and some L ≥ 0 such that d ( T x, T y ) ≤ k d ( x, y ) + L d ( y, T x ), (1). for all x, y ∈ X. Then Fix ( T ) = { x ∈ X : T x = x } ≠ ∅. Theorem 5 (See [25]).
Let ( X, d ) be a complete metric space and T : X → X be an almost contraction, that is, a mapping for which there exist a constant k ∈ ( 0, 1 ) and some L ≥ 0 such that d ( T x, T y ) ≤ k d ( x, y ) + L d ( x, T x ), (2).
