Approximating Solutions of General Class of Variational Inclusions Involving ${\mathcal{B}}^l$-Co-Monotone Mappings in Banach Spaces

The goal of the current study is to introduce a new class of proximal-point mappings that are associated with a new class of ${\mathcal{B}}^l$-co-monotone mappings that are being defined. The ${\mathcal{B}}^l$-co-monotone mapping is the sum of co-coercive and symmetric monotone mappings and an extension of the $C_n$-monotone mapping. The investigation is further discussed, along with its application, which involves a variational inclusion problem (VIP) in Banach spaces. Moreover, the study proposes an iterative algorithm and systematically investigates the convergence characteristics of its generated sequences. For the purpose of illustrating our findings, a simplified numerical example is created to show the convergence graph by using the MATLAB 2015a.