Results of generalized equilibrium problems with trifunction

The branch of mathematics that deals with equilibrium issues is just a few decades old, allowing us to investigate and solve problems in a wide variety of scientific domains, including but not limited to pure and applied sciences. The thesis here says first, findings for a novel state of the trifunctional for equilibrium problem GP(H,L_1,L_2 )on convex and closed sets that are either bounded or unbounded in Banach spaces are introduced. This is done by employing a generalized form of monotonicity known as ϑL-g - monotone are introduced. Second, it explores certain findings associated with this subject and defines and expands the idea of hemiequilibrium issues.