The Yosida approximation iterative technique for split monotone Yosida variational inclusions

A different approach to approximating solutions of monotone Yoshida variational inclusion problem in a Banach space

“…We prove a strong convergence theorem of the aforementioned problem. Our result extends and complements the result of [13], [22], [25] and other related results in literature.…”

“…al. [25] introduced the Split Monotone Yosida Variational Inclusion Problem (SMYVIP) which is to find a point…”

“…al. [25] presented the following Yosida approximation technique to approximate the solution of SMYVIP (15)- (16).…”

“…is the Yosida approximation operator of the mapping B, R B µ = (I + µB) −1 is the resolvent of multivalued maximal monotone mapping B for µ > 0 and I is the identity mapping on Hilbert space E. In this article, we consider the following problems: (i) Can we introduce the MYVIP considered in [25] to a p-uniformly convex and uniformly smooth Banach space? (ii) Can we approximate the solution of MYVIP (17) using a different method of proof different from the ones considered in [1,5,9,14,13,24]?…”

“…al. [25], Ogbuisi and Mewomo [24], we introduce an Halphern-type iterative method for approximating the solution of MYVIP (17) in the framework of p-uniformly convex and uniformly smooth Banach space. We prove a strong convergence theorem of the aforementioned problem.…”