Throughout the years, equilibrium problems have been used to
study various problems appearing in different fields of mechanics, physics,
nonlinear programming, engineering mathematics, and so on (see for example, [7], [12]). Consequently, lots of research has been done on solving equilibrium problems under
different circumstances in reflexive Banach spaces. This paper contemplates a
generalized category of equilibrium problems on Hadamard manifolds called
hemiequilibrium problems (HEP). We initiate the existence of solutions to
hemiequilibrium problems (HEP) under the monotonicity assumption on the
underlying bifunction by applying the KKM technique. We construct some
counterexamples in the Hadamard manifold to rationalize our efforts. Additionally, we investigate a few iterative algorithms to solve hemiequilibrium problems on these nonlinear domains. Some particular instances of hemiequilibrium problems are demonstrated. These general classes of equilibrium problems are new on Hadamard manifolds. We hope our outcomes and ideas will
spark further investigation in this fascinating and captivating field of research.