This paper introduces a new meta-heuristic technique, named geometric mean optimizer (GMO) that emulates the unique properties of operator in mathematics. can simultaneously evaluate fitness and diversity search agents space. In GMO, scaled objective values certain agent’s opposites is assigned to agent as its weight representing overall eligibility guide other process when solving an optimizat...

We establish some new properties of spectral geometric mean. In particular, we prove a log majorization relation between (Bts/2A(1−t)sBts/2)1/s and the t-spectral mean A♮tB:=(A−1♯B)tA(A−1♯B)t two positive semidefinite matrices A B, where A♯B is mean, dominant one. The limit involving also studied. then extend all results in context symmetric spaces negative curvature.