Approximating fixed points by ishikawa iterates

Approximating fixed points of generalized nonexpansive mappings

Normal Families and Fixed Points of Iterates

Let F be a family of holomorphic functions and suppose that there exists ε > 0 such that if f ∈ F , then |(f2)′(ξ)| ≤ 4 − ε for all fixed points ξ of the second iterate f. We show that then F is normal. This is deduced from a result which says that if p is a polynomial of degree at least 2, then p has a fixed point ξ such that |(p2)′(ξ)| ≥ 4. The results are motivated by a problem posed by Yang...

Ishikawa Iteration with Errors for Approximating Fixed Points of Strictly Pseudocontractive Mappings of Browder-Petryshyn Type

Let q > 1 and E be a real q−uniformly smooth Banach space. Let K be a nonempty closed convex subset of E and T : K → K be a strictly pseudocontractive mapping in the sense of F. E. Browder and W. V. Petryshyn [1]. Let {un} be a bounded sequence in K and {αn}, {βn}, {γn} be real sequences in [0,1] satisfying some restrictions. Let {xn} be the bounded sequence in K generated from any given x1 ∈ K...

New iteration process for approximating fixed points in Banach spaces

‎The object of this paper is to present a new iteration process‎. ‎We will show that our process is faster than the known recent iterative schemes‎. ‎We discuss stability results of our iteration and prove some results in the context of uniformly convex Banach space for Suzuki generalized nonexpansive mappings‎. ‎We also present a numerical example for proving the rate of convergence of our res...

approximating fixed points of generalized nonexpansive mappings