By using Lim’s inequalities, Nadler’s results, the new parametric resolvent operator technique associated with (A,η,m)(A,η,m)-maximal monotone operators, in this paper, the existence theorem for a new class of generalized nonlinear parametric (A,η,m)(A,η,

The unit sphere in an infinite dimensional Banach space is a lipschitzian retract of the unit ball. The aim of this paper is to present a new upper bound for the optimal retraction constant in some classical Banach spaces. In particular, an improved estimate from above is obtained for the space C[0,1]