Darte et al. proposed a lattice-based mathematical framework for array mapping, establishing a correspondence between valid linear storage allocations and integer lattices called strictly admissible [13].
The first five frequency parameters of this beam obtained by using the Rayleigh-Ritz method in conjunction with broadly admissible base beam eigenfunctions, Galerkin's method in conjunction with strictly admissible base beam eigenfunctions, and the classical finite element method, are compared with the exact ones over a wide range of values of the system parameters.
Since T is strictly α-admissible, we have (alpha (x_{n},x_{n+1})>1) for all (ninmathbb{N}).
In [18], the authors introduced the following notion of strictly α-admissible.
Since T is strictly α-admissible, we have (alpha(x_{1},x_{2})>1}.
Since T is strictly α-admissible, we deduce that (alpha (x_{1},x_{2})=h_{1}>1).
T is strictly α-admissible; for each (x,yin X), alpha x,y mathcal{H}_{p}(Tx,Ty leqvarphibigl(p x,y bigr).
We say that T is strictly α-admissible if α ( x, y ) > 1 implies that α ( y, z ) > 1, x ∈ X, y ∈ T x, z ∈ T y.
We say that T is strictly α-admissible if alpha x,y)>1 quadmbox{implies} quad alpha y,z >1,quad xin X, yin Tx, zin Ty.
So, we can obtain a sequence x n ∈ X recursively as follows: x n ∈ T x n − 1 for all n ∈ N. Since T is strictly α-admissible, we deduce that α ( x 1, x 2 ) = k 1 > 1. Continuing this process, we have that α ( x n, x n + 1 ) = k n > 1 for all n ∈ N ∪ { 0 }.
We first introduce the following notions of a strictly α-admissible and and an α-Meir-Keeler contraction with respect to the partial Hausdorff metric H p. Definition 5 Let ( X, p ) be a partial metric space, T : X → CB p ( X ) and α : X × X → R + ╲ { 0 }.
