An iterative algorithm for approximating solutions of Hammerstein equations with monotone maps in Banach spaces

A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications

“…Convergence of the sequence {v n } with initial point (5,8) Remark 5 Our theorem is a significant improvement of the results of Diop et al [33], Chidume and Bello [20], Chidume [18], Chidume et al [26], and Chidume et al [24] in the following sense:…”

“…Lemma 2.2 (Chidume [18]) Let X be a uniformly convex real Banach space. For arbitrary r > 0, let B r (0) := {u ∈ X : u ≤ r}.…”

“…(1) Theorems 3.1 and 5.2 are proved in a more general real Banach space which contains the space of 2-uniformly convex space and L P spaces, 1 < p < ∞. (2) The class of strongly monotone maps studied in Diop et al [33], Chidume and Bello [20] is extended to the more general class of generalized-Φ-strongly monotone maps in Theorems 3.1 and 5.2, respectively. (3) The requirement that the maps A, K , and F be bounded, which is assumed in Theorems 1.1 and 3.1 of Diop et al [33], Chidume and Bello [20], respectively, and in the theorem of Chidume et al [24,26] and Chidume [18], is dispensed with in our theorems.…”

Algorithms for Hammerstein inclusions in certain Banach spaces

“…Using the same scheme, still in [22], they also proved a similar result in L p , for 2 p < ∞. Let E be a normed linear space.…”

“…Recently, Chidume and Bello [22] constructed a new iterative algorithm for approximating solutions of Hammerstein equations in L p -spaces, and where the operators K and F are assumed to be bounded and strongly monotone. They obtained the following theorem.…”