In the present work, we introduce a new hybrid iterative process which is combination of proximal point algorithms and modified Krasnoselskii-Mann algorithm for approximating common element set minimizers convex function fixed points finite family multivalued strictly pseudo-contractive mappings in framework Hilbert spaces. We then prove strong convergence proposed without imposing any compactn...

Opial presented in 1967 a theorem, which can be applied in order to prove the weak convergence of sequences (xk) in a Hilbert space, generated by iterative schemes of the form xk+1 = Uxk for a nonexpansive and asymptotically regular operator U with nonempty FixU . Several iterative schemes have, however, the form xk+1 = Ukxk, where (Uk) is a sequence of operators with a common fixed point. We s...

Let T be a (possibly nonlinear) continuous operator on Hilbert space H. If, for some starting vector x , the orbit sequence {T k x, k = 0, 1, . . .} converges, then the limit z is a fixed point of T ; that is, T z = z. An operator N on a Hilbert space H is nonexpansive (ne) if, for each x and y in H, ‖Nx − Ny‖ ‖x − y‖. Even when N has fixed points the orbit sequence {Nk x} need not converge; co...

We study Krasnoselskii-Mann style iterative algorithms for approximating fixpoints of asymptotically weakly contractive mappings, with a focus on providing generalized convergence proofs along explicit rates convergence. More specifically, we define new notion being ψ-weakly modulus, and present series abstract theorems which both generalize unify known results from the literature. Rates are fo...

Based on the very recent work by Censor-Gibali-Reich [7], we propose an extension of their new variational problem (Split Variational Inequality Problem) to monotone variational inclusions. Relying on the Krasnoselskii-Mann Theorem for averaged operators, we analyze an algorithm for solving a new split monotone inclusions under weaker conditions. Our results improve and develop previously discu...

In this paper, we introduce and study a class of new Picard-Mann iterative methods with mixed errors for common fixed points of two different nonexpansive and contraction operators. We also give convergence and stability analysis of the new Picard-Mann iterative approximation and propose numerical examples to show that the new Picard-Mann iteration converges more effectively than the Picard ite...