As a result, cases of malaria and TB have declined in recent decades with cases of contractions amongst Bahraini nationals becoming rare.
This question has been answered in the positive, in the case of contraction condition (1), by Ostrowski [2], who established the first stability result for a fixed point iteration procedure, by using the following estimate: d ( y n, p ) ≤ α n 1 − α d ( x 0, x 1 ) + ∑ k = 1 n α n − k ϵ k, n = 0, 1, 2, …, (2).
It is easy to prove that a pointwise contraction T : C → C has a fixed point in the same way as in the case of contractions.
However, in the case of contractions and in the case of dissipative operators one has to consider double operator integrals with respect to semi-spectral measures.
In cases of large contraction ratios of magnetospheric magnetic tubes, the wave energy flux at the ionospheric boundary can be rather small.
In fact, Meir-Keeler contractions [25, 26], (mathcal{Z} -contractions [18, 19], manageable contractions [27], and Geraghty contractions [5] are particular cases of R-contractions.
The Banach contractions are particular cases of F-contractions, where F ( t ) = ln t.
Remark 2.1 Since each nonlinear contraction includes the case of linear contraction as its special case, each fixed point theorem in the above theorem implies a fixed point theorem for linear contraction.
It is seen that, in all cases, the behaviour of contraction time estimated with the four signals is very similar (although the MEAN difference of the SVN test of the first dog is unsatisfactorily great, as seen in Table 2).
Wardowski deduced that the Banach contractions are particular case of F-contractions and the author supported his finding by presenting some F-contractions which are not Banach contractions.
