Some Convergence Results for the Solution of New Type of Variational Inequalities Associated with Generalized Pseudo-Monotone Mappings in Complete CAT (0) Spaces (European Journal of Pure and Applied Mathematics, 2025)
The basic purpose of this article is to introduce a generalized version of pseudo-monotone variational inequality in the setting of complete $\mathcal{CAT}(0)$ spaces and to present some strong and $Δ$-convergence results for the existence of solutions for the respective variational inequality problem. Algorithm 1 and 2 are proposed in accordance with pseudo-monotone and $α$-strongly pseudo-monotone mappings to prove our results under some conditions. A numerical implication of our proposed algorithm is also presented.
Keywords: projection type method; variational inequality; pseudo-monotone mapping