modified halpern iteration of asymptotically non-expansive mappings

Modified Halpern Iteration of Asymptotically Non-Expansive Mappings

A Modified Halpern-Type Iteration for Bregman Relatively Nonexpansive Mappings

We introduce a new modified Halpern-type iteration for a family of Bregman relatively nonexpansive mappings and establish strong convergence theorems in reflexive Banach spaces. The results extend the corresponding results obtained by many authors. Mathematics Subject Classification: 47H09; 47H10

New Hybrid Algorithm of Modified Halpern Iteration Scheme for Quasi-φ-nearly Asymptotically Nonexpansive Mappings in Banach Spaces

In this paper, we introduce a new hybrid algorithm of modified Halpern iteration for a countable infinitely family of quasi-φ-nearly asymptotically nonexpansive mappings in Banach spaces and prove the strong convergence for the proposed algorithm. Our proof method is of novelty and the results presented in this paper improve the corresponding ones announced by others. Mathematics Subject Classi...

Convergence and Stability of Modified Random SP-Iteration for A Generalized Asymptotically Quasi-Nonexpansive Mappings

The purpose of this paper is to study the convergence and the almost sure T-stability of the modied SP-type random iterative algorithm in a separable Banach spaces. The Bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure T-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. Our result...

Modified Mann-Halpern Algorithms for Pseudocontractive Mappings

and Applied Analysis 3 We know that T is pseudocontractive if and only if T satisfies the condition 󵄩󵄩󵄩Tx − Ty 󵄩󵄩󵄩 2 ≤ 󵄩󵄩󵄩x − y 󵄩󵄩󵄩 2 + 󵄩󵄩󵄩(I − T)x − (I − T)y 󵄩󵄩󵄩 2 (15) for all x, y ∈ C. Since u ∈ Fix(T), we have from (15) that ‖Tx − u‖ 2 ≤ ‖x − u‖ 2 + ‖x − Tx‖ 2 , (16) for all x ∈ C. By using (13) and (16), we obtain 󵄩󵄩󵄩Tyn − u 󵄩󵄩󵄩 2 ≤ 󵄩󵄩󵄩yn − u 󵄩󵄩󵄩 2 + 󵄩󵄩󵄩yn − Tyn 󵄩󵄩󵄩 2 = 󵄩󵄩󵄩(1 − γn)xn + γnT...

convergence and stability of modified random sp-iteration for a generalized asymptotically quasi-nonexpansive mappings

the purpose of this paper is to study the convergence and the almost sure t-stability of the modied sp-type random iterative algorithm in a separable banach spaces. the bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure t-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. our resu...