In this paper, we obtained the convergence of modified Noor iterative scheme for nearly Lipschitzian maps in real Banach spaces. Our results contribute to the literature in this area of re- search.

Jaggi and Kassay proved that for reflexive Banach spaces X, normal structure is equivalent to the Jaggi fixed point property (i.e. all Jagginonexpansive maps on closed, bounded, convex sets in X have a fixed point); which we note is equivalent to a natural variation: the Jaggi* fixed point property. In the spirit of this result, we prove that for all Banach spaces X, uniform normal structure is...

LetK be a nonempty closed convex subset of a real Banach space E, T : K → K a uniformly L-Lipschitzian asymptotically pseudocontractive mapping with sequence {kn}n≥0 ⊂ [1,∞), lim n→∞ kn = 1 such that p ∈ F (T ) = {x ∈ K : Tx = x}. Let {an}n≥0, {bn}n≥0 , {cn}n≥0 be real sequences in [0, 1] satisfying the following conditions: (i) an + bn + cn = 1; (ii) ∑ n≥0 bn =∞; (iii) cn = o(bn); (iv) lim n→∞...

Fixed point theorems for generalized Lipschitzian semigroups are proved in puniformly convex Banach spaces and in uniformly convex Banach spaces. As applications, its corollaries are given in a Hilbert space, in Lp spaces, in Hardy space Hp , and in Sobolev spaces Hk,p , for 1<p <∞ and k≥ 0.

We show that the variational inequality $VI(C,A)$ has aunique solution for a relaxed $(gamma , r)$-cocoercive,$mu$-Lipschitzian mapping $A: Cto H$ with $r>gamma mu^2$, where$C$ is a nonempty closed convex subset of a Hilbert space $H$. Fromthis result, it can be derived that, for example, the recentalgorithms given in the references of this paper, despite theirbecoming more complicated, are not...

Let (X,‖ · ‖) be an infinite-dimensional Banach space with the unit ball B and the unit sphere S. Since the works of Nowak [11], Benyamini and Sternfeld [1], and Lin and Sternfeld [10], it is known that S is a Lipschitzian retract of B. It means that there exists a mapping (retraction) R : B → S satisfying Rx = x for all x ∈ S and also being Lipschitzian. If R satisfies the Lipschitz condition ...