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Linking (1) and (3), we have begin{aligned} e_{k+1}(t)= I-BP_{o})e_{k}(t)+g bigl(t,x_{k}(t)bigr)-gbigl(t,x_{k+1}(t)bigr)+eta _{k}(t)-eta_{k+1}(t). end{aligned} (5) Taking the norm (|cdot|) on both sides of (5), one can derive that begin{aligned} biglVert e_{k+1}(t)bigrVert leq Vert I-BP_{o}Vert biglVert e_{k}(t)bigrVert +L_{g}biglVert Delta x_{k}(t)bigrVert +d_{eta}.

one can derive that (2.6).

Combining the above inequalities, one can derive that (3.8).

by the definition of f n and passing to limit in (3.4), one can derive that ∥ v ∥ 0 = 1.

end{aligned} (8) On the other hand, repeat a proof similar to that in Lemma 2.3(i), Lemma 2.4(i), and one can derive that begin{aligned} bigglvert int_{T epsilon)}^{t} t-s)^{mu+nu-1} t-shbb{E}_{mu+nu,mu+nu } bigl(-(t-s)^{mu+nu}lambda_{1} bigr),ds biggrvert leq B(mu,nu,lambda_{1},lambda_{2}).

Let us define an (mathcal{R}) function (varphi: [0,infty ) rightarrow[0,1)) by varphi(t) = a + 2b + 2c quad text{for all } t in [0,infty). Then one can derive that the relation (3.12) is transformed to (3.1), and so the required result follows immediately from Theorem 3.1. □. Next, motivated by the idea of Berinde [18], we now present another fuzzy fixed point theorem.

However, by (31 - 34 31 - 34eorem 1, we candderive Theorem0) has one unique equilibrium solution which is globally exponentially stable.

we can derive that (2.15).

Then, one can derive from that (3..14).

Molecular descriptors and graph theoretical descriptors can be used effectively to derive such relationships and when done properly, one can derive mathematical models that are predictive and allow the modeler to be involved in computer-aided molecular design (CAMD).

Even before a lead candidate is found, such requirements can be summarised in an intended performance profile, and from that profile one can derive the required characteristics that will help ensure the development of a high quality therapeutic candidate.