On an equation of linear iteration

Convex solutions of polynomial-like iterative equations

“…Equation (1.1) has been studied extensively when X = R (see [1]). For linear F it was researched in [3,5,[9][10][11][12][13]17,18]. For nonlinear F , increasing solutions for n = 2 were discussed in [22] by constructing uniformly convergent sequences.…”

On set-valued solution of an n-order iterative functional equation

“…The problem of the existence, uniqueness and stability of solution for Eq. (1.1) in several classes of single-value function were investigated, e.g., in [2][3][4][5][6][7][8]). Recently set-valued solutions of some equations were investigated by some authors( cf., e.g., [9][10][11]).…”

Convex solutions to polynomial-like iterative equations on open intervals

“…, λ n are real constants, F : S → S is a given function, while f : S → S is the unknown function. There exists a rich literature concerning polynomial-like iterative equations (see, for instance, [6,8,[14][15][16][17][18][19]). Especially, we point out here the papers by Zhang et al [19] and by Xu and Zhang [16], dealing with the existence of monotonic or convex solutions to Eq.…”