An inertial algorithm for solving Hammerstein equations is presented. This obtained as a consequence of new proposed and studied nonlinear involving operators that are m-accretive. Some strong convergence theorems proved in real Banach spaces uniformly smooth. Furthermore, comparisons the numerical performance our algorithms with some recent important

In this paper, we introduce a general viscosity-type extragradient method for solving the fixed point problem of an asymptotically nonexpansive mapping and variational inclusion with two accretive operators. We obtain strong convergence theorem in setting Banach spaces. terms theorem, establish result (FPP) inequality (VIP) inverse-strongly monotone framework Hilbert Finally, is applied to deal...

We consider the Riesz transforms ∇L−1/2, where L ≡ −divA(x)∇, and A is an accretive, n× n matrix with bounded measurable complex entries, defined on Rn. We establish boundedness of these operators on Lp(Rn), for the range pn < p ≤ 2, where pn = 2n/(n + 2), n ≥ 2, and we obtain a weak-type estimate at the endpoint pn. The case p = 2 was already known: it is equivalent to the solution of the squa...

Let E be a real reflexive and strictly convex Banach space which has a uniformly Gâteaux differentiable norm and let C be a closed convex nonempty subset of E. Strong convergence theorems for approximation of a common zero of a countably infinite family of m-accretive mappings from C to E are proved. Consequently, we obtained strong convergence theorems for a countably infinite family of pseudo...

Suppose X is a real Banach space and F,K : X → X are accretive maps. Under different continuity assumptions on F and K such that the inclusion 0 = u+KFu has a solution, iterative methods are constructed which converge strongly to such a solution. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X . Our method of proof is of independ...

We investigate the equivalence between the convergences of the Mann iteration method and the Ishikawa iteration method with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces. A related result deals with the equivalence of theMann iterationmethod and the Ishikawa iterationmethod for φ-pseudocontractive operators in nonempty closed convex subsets of unifor...