ON THE CONVERGENCE OF SOLUTIONS TO A DIFFERENCE INCLUSION ON HADAMARD MANIFOLDS.

The aim of this paper is to study the convergence of solutions of the following second order difference inclusion { exp-1ui ui+1 + θi exp-1ui ui-1 ∊ ciA(ui), i ≥ 1 u0 = x ∊ M; sup i≥0 d(ui, x) < +∝, to a singularity of a multi-valued maximal monotone vector field A on a Hadamard manifold M, where {ci} and {θi} are sequences of positive real numbers and x is an arbitrary fixed point in M. The results of this paper extend previous results in the literature from Hilbert spaces to Hadamard manifolds for general maximal monotone, strongly monotone multi-valued vector fields and subdifferentials of proper, lower semicontinuous and geodesically convex functions f : M →] - ∝,+∝]. In the recent case, when A = ϐf, we show that the sequence {ui}, given by the equation, converges to a point of the solution set of the following constraint minimization problem Min x∊M f(x). [ABSTRACT FROM AUTHOR]