ISHIKAWA ITERATION WITH ERRORS FOR APPROXIMATING FIXED POINTS OF STRICTLY PSEUDOCONTRACTIVE MAPPINGS OF BROWDER-PETRYSHYN TYPE

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...

Strong Convergence Theorems of the Ishikawa Process with Errors for Strictly Pseudocontractive Mapping of Browder-Petryshyn Type in Banach Spaces

We prove several strong convergence theorems for the Ishikawa iterative sequence with errors to a fixed point of strictly pseudocontractive mapping of Browder-Petryshyn type in Banach spaces and give sufficient and necessary conditions for the convergence of the scheme to a fixed point of the mapping. The results presented in this work give an affirmative answer to the open question raised by Z...

An Iterative Algorithm on Approximating Fixed Points of Pseudocontractive Mappings

Let E be a real reflexive Banach space with a uniformly Gâteaux differentiable norm. Let K be a nonempty bounded closed convex subset of E, and every nonempty closed convex bounded subset of K has the fixed point property for non-expansive self-mappings. Let f : K → K a contractive mapping and T : K → K be a uniformly continuous pseudocontractive mapping with F T / ∅. Let {λn} ⊂ 0, 1/2 be a seq...

Approximating fixed points of generalized nonexpansive mappings

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...