Convergence of a Halpern-type iteration algorithm for a class of pseudo-contractive mappings

An explicit iterative algorithm for k -strictly pseudo-contractive mappings in Banach spaces

“…More precisely, he weakened the condition (iii) by removing the square in the denominator so that the choice of α n = 1 n+1 is possible. Chidume and De Souza [4] established a strong convergence theorem for strictly pseudo-contraction in Banach space scheme, the result is as follows:…”

“…Motivated by the results of Chidume and De Souza [4] and the above other works, in this paper, we establish a new iteration process in Banach space scheme as follows:…”

Strong Convergence Theorems for Two Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces

“…Recently, many authors improved and generalized the results of Halpern [11] by means of different methods; see, for example, [2,4,10,[12][13][14][15][16][17] and the references therein. In general, there are two ways as follows.…”

“…Motivated and inspired by [2,4,10,[12][13][14][15][16][17], the purpose of this paper is to modify Halpern iteration (2) by means of both methods above for two total quasi--asymptotically nonexpansive mappings and then to prove the strong convergence in the framework of Banach spaces. The results presented in this paper extend and improve the corresponding results of Martinez-Yanes and Xu [15], Plubtieng and Ungchittrakool [16], Qin et al [17], and others.…”

Strong convergence of viscosity approximation methods with strong pseudocontraction for Lipschitz pseudocontractive mappings

“…Chidume-Souza [6] showed several strongly convergent theorems of the iteration (1.6) for Lipschitz pseudocontractive mappings in a real reflexive Banach space E with a uniformly Gâteaux differentiable Vol. 13 (2009) Lipschitz pseudocontractive mappings 645 norm and with the fixed point property for nonexpansive self-mappings: for any u, x 1 ∈ K, In this paper, we deal with iterative schemes generated by (1.7) for a Lipschitz pseudocontractive mapping T and a fixed Lipschitz strongly pseudocontractive mapping f : n αn = 0, which is one of the generalized results of main results of Chidume-Udomene [13] and Schu [32] and Chidume-Souza [6] and Zhou [47] and ChidumeOfoedu [14] and Song [34] and others. In particular, the parameters of our iterative sequence are simpler, and the typical example is α n = β n = 1 n+1 .…”