There are many convex metric spaces which are not normed linear spaces (see [5, 6]).
On the other case, our presented fixed point theorems for mappings under contractive conditions expressed in the terms of w-distance can be applied, although the underlying cone is not normed.
If (p>1), then (L_{p,phi}(beta_{1},infty)) and (l_{q,psi}) are normed spaces; if (0< p<1) or (p<0), then both (L_{p,phi }(beta_{1},infty)) and (l_{q,psi}) are not normed spaces, but we still use the formal symbols in the following.
Thus all hypotheses of our Theorem 9 are satisfied and z = 0 is a fixed point of T. Note that the mapping T : X → X satisfies the condition (2.1) in the main Theorem 2.2 of Wang and Guo[14]with g(x) = x and a1 = 1/ 2, a2 = a3 = a4 = 0, but Theorem 2.2 cannot be applied since a cone P is not normed.
They proved a common fixed point theorem (Theorem 2.2) by using c-distance in a cone metric space (X, d), where a cone P is normal with normal constant K. Now we shall present an example (Example 7 below), which shows that there are cone metric spaces where underlying cone is not normed, and so theorems of Wang and Guo[14]cannot be applied.
As the BPVS is not normed for adults, it is not possible to identify whether impairments were beyond or in-line with intellectual function.
The following is an example of a hyperbolic space that is not a normed space.
We now give another example where is a metrizable linear topological vector space that is not a normed linear space.
We see that (({{mathbb{R}}}_{{mathcal{F}}},oplus,odot, Vert cdot Vert )) is not a normed space because (({{mathbb{R}}}_{{mathcal{F}}},oplus )) is not a group.
Notice that X is not a normed vectorial space if v ≠ 0. Nevertheless, if v ≠ 0, X is an affine space and hence it is an ANR.
