Note that since g is an isometry, it is continuous.
Since T is continuous, from the well known result in -fuzzy (probabilistic) normed space (see, [51, Chap.
Since T is continuous, from the well-known result in an L -fuzzy (probabilistic) normed space (see [31], Chapter 12), it follows that.
Now, since F is continuous, from (16) and using Lemma 2.1, we get lim n → + ∞ p ( F ( F x n ), F x ) = p ( F x, F x ).
(2.25) Since F is continuous from the right, there exists a real number (h>1) such that Fbigl(hH(Tx_{n},Tx bigr)< Fbigl(H(Tx_{n},Tx bigr)+tau.
end{aligned} Since F is continuous from the right, so there exists a real number (h>1) such that Fbigl(hH(Tx_{n},Tx bigr)< Fbigl(H(Tx_{n},Tx bigr)+tau.
From the assumption, we have 2tau+Fbigl(H(Tx_{0},Tx_{1} bigr)leq F bigl(d(x_{0},x_{1} bigr). Since F is continuous from the right, there exists a real number (h>1) such that Fbigl(hH(Tx_{0},Tx_{1} bigr)leq Fbigl(H(Tx_{0},Tx_{1}) bigr)+tau.
Since is continuous from relations (3.48) and (3.49) it follows that.
It is continuous and dynamic.
for all, and since the mapping is continuous from to itself (cf. [29]), we can pass to the upper limit on the right-hand side for.
end{aligned} Since (k(cdot, x)) is continuous (from (H2)(ii)) and μ is continuous, it follows that (Vert Cx(t_{n} ) - Cx t Vert longrightarrow0).
