Newton-type methods for quasidifferentiable equations

In this paper, we present two Newton-type methods for solving quasidifferen tiable equations in the sense of Demyanov and Rubinov (Ref. 1). Method I is well defined and is a natural extension of the classical Newton method, ba sed on a generalized Kakutani fixed-point theorem. Method II is a simplifie d version and requires less computation than Method I. Under some mild assu mptions, we establish a locally quadratic convergent theorem for Method I a nd prove a semilocal convergence theorem for Method II.