Abstract In this paper, we propose a modified proximal point algorithm based on the Thakur iteration process to approximate common element of set solutions convex minimization problems and fixed points two nearly asymptotically quasi-nonexpansive mappings in framework $\operatorname{CAT}(0)$ CAT ( <mml:m...

Determining xed points of nonexpansive mappings is a frequent problem in mathematics and physical sciences. An algorithm for nding common xed points of nonexpansive mappings in Hilbert space, essentially due to Halpern, is analyzed. The main theorem extends Wittmann's recent work and partially generalizes a result by Lions. Algorithms of this kind have been applied to the convex feasibility pro...

with kn ≥ 0, rn ≥ 0, kn → 1, rn → 0 n → ∞ , for each x, y ∈ C, n 0, 1, 2, . . . . If kn 1 and rn 0, 1.1 reduces to nonexpansive mapping; if rn 0, 1.1 reduces to asymptotically nonexpansive mapping; if kn 1, 1.1 reduces to asymptotically nonexpansive-type mapping. So, a generalized asymptotically nonexpansive mapping is much more general than many other mappings. Browder 1 introduced the followi...

The purpose of this paper is to propose an algorithm for solving the split feasibility problems for total quasi-asymptotically nonexpansive mappings in infinite-dimensional Hilbert spaces. The results presented in the paper not only improve and extend some recent results of Moudafi [Nonlinear Anal. 74:4083-4087, 2011; Inverse Problem 26:055007, 2010], but also improve and extend some recent res...

Let E be a real Banach space, K a closed convex nonempty subset of E, and T1,T2, . . . ,Tm : K → K asymptotically quasi-nonexpansive mappings with sequences (resp.) {kin}n=1 satisfying kin → 1 as n → ∞, and ∑∞ n=1(kin − 1) < ∞, i = 1,2, . . . ,m. Let {αn}n=1 be a sequence in [ , 1− ], ∈ (0,1). Define a sequence {xn} by x1 ∈ K , xn+1 = (1− αn)xn + αnT n 1 yn+m−2, yn+m−2 = (1− αn)xn + αnT 2 yn+m−...

and Applied Analysis 3 4 if E is a reflexive, strictly convex, and smooth Banach space, then for all x, y ∈ E, φ ( x, y ) 0 iff x y. 1.7 For more details see 2, 3 . Let C be a closed convex subset of E, and let T be a mapping from C into itself. We denote by F T the set of fixed point of T . A point p in C is said to be an asymptotic fixed point of T 8 if C contains a sequence {xn}which converg...

It is defined a class of generalized nonexpansive mappings, which properly contains those by Suzuki in 2008, and that preserves some its fixed point results.