A Halpern-Type Iteration Method for Bregman Nonspreading Mapping and Monotone Operators in Reflexive Banach Spaces
Joint Authors
Isiogugu, F. O.
Ogbuisi, F. U.
Jolaoso, L. O.
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-09-02
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
In this paper, we introduce an iterative method for approximating a common solution of monotone inclusion problem and fixed point of Bregman nonspreading mappings in a reflexive Banach space.
Using the Bregman distance function, we study the composition of the resolvent of a maximal monotone operator and the antiresolvent of a Bregman inverse strongly monotone operator and introduce a Halpern-type iteration for approximating a common zero of a maximal monotone operator and a Bregman inverse strongly monotone operator which is also a fixed point of a Bregman nonspreading mapping.
We further state and prove a strong convergence result using the iterative algorithm introduced.
This result extends many works on finding a common solution of the monotone inclusion problem and fixed-point problem for nonlinear mappings in a real Hilbert space to a reflexive Banach space.
American Psychological Association (APA)
Ogbuisi, F. U.& Jolaoso, L. O.& Isiogugu, F. O.. 2019. A Halpern-Type Iteration Method for Bregman Nonspreading Mapping and Monotone Operators in Reflexive Banach Spaces. Journal of Mathematics،Vol. 2019, no. 2019, pp.1-11.
https://search.emarefa.net/detail/BIM-1181408
Modern Language Association (MLA)
Ogbuisi, F. U.…[et al.]. A Halpern-Type Iteration Method for Bregman Nonspreading Mapping and Monotone Operators in Reflexive Banach Spaces. Journal of Mathematics No. 2019 (2019), pp.1-11.
https://search.emarefa.net/detail/BIM-1181408
American Medical Association (AMA)
Ogbuisi, F. U.& Jolaoso, L. O.& Isiogugu, F. O.. A Halpern-Type Iteration Method for Bregman Nonspreading Mapping and Monotone Operators in Reflexive Banach Spaces. Journal of Mathematics. 2019. Vol. 2019, no. 2019, pp.1-11.
https://search.emarefa.net/detail/BIM-1181408
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1181408