Iterative Algorithms for Split Common Fixed Point Problem Involved in Pseudo-Contractive Operators without Lipschitz Assumption

oleh: Jinzuo Chen, Mihai Postolache, Li-Jun Zhu

Format: Article
Diterbitkan: MDPI AG 2019-08-01

Deskripsi

Two iterative algorithms are suggested for approximating a solution of the split common fixed point problem involved in pseudo-contractive operators without Lipschitz assumption. We prove that the sequence generated by the first algorithm converges weakly to a solution of the split common fixed point problem and the second one converges strongly. Moreover, the sequence <inline-formula> <math display="inline"> <semantics> <mrow> <mo>{</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>}</mo> </mrow> </semantics> </math> </inline-formula> generated by Algorithm 3 strongly converges to <inline-formula> <math display="inline"> <semantics> <mrow> <mi>z</mi> <mo>=</mo> <msub> <mi>proj</mi> <mi>S</mi> </msub> <mn>0</mn> <mo>,</mo> </mrow> </semantics> </math> </inline-formula> which is the minimum-norm solution of problem (1). Numerical examples are included.