Furthermore, the property defined on the underlying operator T depends on the mapping g in convergence analysis.
To obtain the least convex solution of (8) in ([alpha,beta ]), we only have to redefine the mapping G in the obvious way.
Also, in our results the mapping g is not required to be continuous, but the condition is imposed on the mapping g in the results of Sedghi et al. and Hu.
(iv) The iterative scheme (3.1) in Theorem 3.1 is very different from any in [[22], Theorem 3.1], [[2], Theorem 3.1] and [[3], Theorem 3.1], because the mapping G in [[3], Theorem 3.1] and the mapping J r n in [[22], Theorem 3.1] are replaced by the same composite mapping J r n G in the iterative scheme (3.1) of our Theorem 3.1.
On the other hand, define (P :Z rightrightarrows Y) by P x):=Y setminus G x) (2) for each (x in Z), and define (Q, R, S, T:Z rightrightarrows Y) similarly, with the mapping G in (2) replaced by F, E, D, and C, respectively.
(iv) The iterative scheme (4.1) in Theorem 4.1 is very different from any in [[22], Theorem 3.1], [[2], Theorem 3.1] and [[3], Theorem 3.1] because the mapping J r n in [[22], Theorem 3.1] and the mapping G in [[3], Theorem 3.1] are replaced by the same composite mapping J r n G in the iterative scheme (4.1) of Theorem 4.1.
A map g in (mathsf{Ind},mathcal {C}) lies in the class W if (g=f circ c) with (f in overline{F}) and (c in overline{C}).
Therefore no (I_{g}) given by a weakly unimodal map g in Theorem 1 or Theorem 2 is homeomorphic to (X_{f}).
Suppose (X_{F}) is homeomorphic to (I_{g}), given by a weakly unimodal map g in Theorem 1 or Theorem 2.
A map F in L ∂ u ( U ¯, Y ) is essential if every map G in L ∂ u ( U ¯, Y ) such that G | ∂ U = F | ∂ U has a fixed point in U.
Define a mapping G as in Lemma 2.10 and for every λ A ∈ ( 0, α K 2 ), λ B ∈ ( 0, β K 2 ) and a ∈ ( 0, 1 ) where K is 2-uniformly smooth constant.
