TY - JOUR
T1 - The generalized contraction proximal point algorithm with square-summable errors
AU - Boikanyo, Oganeditse A.
PY - 2017/6/1
Y1 - 2017/6/1
N2 - Let (xn) be a sequence generated by xn+1=αnu+γnxn+δnJβnxn+en for n≥ 0 , where Jβn is the resolvent of a maximal monotone operator A with βn∈ (0 , ∞) , u, x0∈ H, (en) is a sequence of errors and αn∈ (0 , 1) , γn∈ (- 1 , 1) , δn∈ (0 , 2) are real numbers such that αn+ γn+ δn= 1 for all n≥ 0. We present strong convergence results for the sequence generated by the generalized contraction proximal point algorithm defined above under weaker accuracy conditions and mild conditions on the parameters αn, βn and δn. Our results generalize and unify many known results in the literature.
AB - Let (xn) be a sequence generated by xn+1=αnu+γnxn+δnJβnxn+en for n≥ 0 , where Jβn is the resolvent of a maximal monotone operator A with βn∈ (0 , ∞) , u, x0∈ H, (en) is a sequence of errors and αn∈ (0 , 1) , γn∈ (- 1 , 1) , δn∈ (0 , 2) are real numbers such that αn+ γn+ δn= 1 for all n≥ 0. We present strong convergence results for the sequence generated by the generalized contraction proximal point algorithm defined above under weaker accuracy conditions and mild conditions on the parameters αn, βn and δn. Our results generalize and unify many known results in the literature.
UR - http://www.scopus.com/inward/record.url?scp=85018355302&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85018355302&partnerID=8YFLogxK
U2 - 10.1007/s13370-016-0453-9
DO - 10.1007/s13370-016-0453-9
M3 - Article
AN - SCOPUS:85018355302
VL - 28
SP - 321
EP - 332
JO - Afrika Matematika
JF - Afrika Matematika
SN - 1012-9405
IS - 3-4
ER -