[PDF] Top 20 Strong convergence of modified Halpern’s iterations for a k strictly pseudocontractive mapping

... Some mathematicians considered the open question. In [], Song proved that for a firmly nonexpansive mapping T , an important subclass of nonexpansive mappings, the answer of the Halpern open problem is ... See full document

... of k-strictly pseudocontractive mapping and the set of zeros of the sum of two monotone operators in a Hilbert ...establish strong convergence of the sequences generated by the ... See full document

... The modified Mann ’ s iteration scheme was introduced by Schu [7,8] and has been used by several authors (see, for example, ...the convergence theorems of modified Mann iteration method in the ... See full document

... new Halpern-type iterative scheme to approximate common fixed points of an infinite family of quasi-nonexpansive mappings and obtain a strongly convergent iterative sequence to the common fixed points of these ... See full document

... space H onto a closed convex subset K of H. It should be noted here that the iteration above works only in a Hilbert space setting. To extend this iteration to a Banach space, the concepts of relatively ... See full document

... The asymptotically nonexpansive mappings have been introduced by Goebel and Kirk in 1972. Since then, a large number of authors have studied the weak and strong convergence problems of the iterative ... See full document

... and K be a nonempty, closed and convex subset of ...weak convergence theorem of the explicit averaging cyclic algorithm for a finite family of asymptotically strictly pseudocontractive mappings ... See full document

... Let E be a smooth, strictly convex, and reflexive Banach space. An operator A : E ® 2 E* is said to be monotone, if 〈x - y, x* - y*〉 ≥ 0 whenever x, y Î E, x* Î Ax, y* Î Ay. We denote the zero point set {x Î E : 0 ... See full document

... space H onto a closed convex subset K of H. It should be noted here that the itera- tion above works only in the Hilbert space setting. To extend this iteration to a Banach space, the concept of relatively ... See full document

... some strong convergence theorems of the modified Ishikawa and Mann iterations with errors of uniformly L-Lipschitzian asymptotically pseudocontractive mappings in real Banach ... See full document

... sunny iff for each x ∈ C and t ∈ (, ), we have Q(tx + ( – t)Qx) = Qx; sunny nonexpansive retraction iff Q sunny, nonexpansive and contraction. K is said to be a nonexpansive re- tract of C if there exists a ... See full document

... the convergence rates of these two iteration ...several strong convergence results in the literature to the class of mappings considered in our ...asymptotically k-strictly ... See full document

... Recently, Su et al. 12 extended the results of Qin and Su 15, Matsushita and Takahashi 14 to a class of closed hemi-relatively nonexpansive mapping. Note that, since the hybrid iterative methods presented by Qin ... See full document

... Theorem . [, Theorem .] Let E be a real q-uniformly smooth Banach space which is also uniformly convex. Let C be a nonempty closed convex subset of E and T : C → C be a k-strictly asymptotically ... See full document

... Fixed point theory in CAT0 spaces was first studied by Kirk see 18, 19. He showed that every nonexpansive single-valued mapping defined on a bounded closed convex subset of a complete CAT0 space always has a fixed ... See full document

... Construction of fixed points of nonexpansive mappings is an important subject in the theory of nonexpansive mappings and its applications in a number of applied areas, in particular, in image recovery and signal ... See full document

... some strong and weak convergence theorems for a continuous pseudocontractive map- ping and a weak convergence theorem for a nonexpansive mapping in real uniformly con- vex Banach ...the ... See full document

... demimetric mapping in CAT(0) space as follows: Let C be a nonempty subset of a complete CAT(0) space X ...a mapping T : C → X is called k-demimetric mapping if F (T ) 6= /0 there exist ... See full document

... It is the purpose of this paper to develop iteration (.) to the processes for nonexpansive mappings, asymptotically nonexpansive mappings, nonexpansive semigroups and asymp- totically nonexpansive semigroups in the ... See full document

... strict pseudocontractive mappings was initiated by Browder and Petryshyn [] in , but the iterative methods for strict pseudocontrac- tive mappings are far less developed than those for nonexpansive ... See full document