Algorithm for zeros of maximal monotone mappings in classical Banach spaces

Algorithm for the solution of Hammerstein integral typ e of equation in a Banach Spaces

“…The operators F and K, defined in 2-uniformly convex and 2uniformly smooth real Banach spaces, are assumed to be bounded, continuous, and monotone. Consequently, the outcomes presented in this study not only expand upon and consolidate the findings of Chidume et al [12], Mendy et al [4], but also encompass a significant portion of the results previously established for this crucial class of nonlinear mappings.…”

“…They find application in various contexts, including functional equations, and often emerge as subdifferentials of convex functions in the field of calculus of variations (see, for example, Pascali and Sburian [39] and Rockafellar [41, page 101]). For the solution of the zeros of A, see Mendy et al [ [5], [3], [9], [7], [8], [31]].…”

“…Notable works in this regard include those by Chidume and Djitte [22,23] as well as Jain et al [17]. For recent advancements utilizing these recursion formulas or their modifications, interested readers are encouraged to refer to the following references: Chidume and Djitte [19][20][21], Chidume and Ofeodu [24], Chidume and Shehu [25],Mendy et al [ [6], [4]] and [18,Chapter 13].…”

“…Inspired by the aforementioned developments, Mendy et al [4] devised and examined the subsequent scheme. They successfully obtained a robust convergence outcome that is comparatively more convenient for real-world implementations when compared to Theorem 1.12.…”

"Solutions of Split Equality Hammerstein Type Equation Problems in Reflexive Real Banach Spaces"

“…Lemma 2.11. [24] Let X be a reflexive real Banach space with dual X * and let A: X → X * be a hemicontinuous monotone mapping. Then, A is maximal monotone.…”