Abstract
In this paper, we give a general inertial Krasnoselskii–Mann algorithm for solving inclusion problems in Banach Spaces. First, we establish a weak convergence in real uniformly convex and q-uniformly smooth Banach spaces for finding fixed points of nonexpansive mappings. Then, a strong convergence is obtained for the inertial generalized forward-backward splitting method for the inclusion. Our results extend many recent and related results obtained in real Hilbert spaces.
Highlights
IntroductionLet X be a real Banach space and given a single and set-valued operators A : X → X and
Let X be a real Banach space and given a single and set-valued operators A : X → X andB : X → 2X, respectively
A known and popular method for solving problem (1) is the forward-backward splitting method [6,7], which is defined in the following manner: x1 ∈ X and xn+1 = JrB, n ≥ 1, (2)
Summary
Let X be a real Banach space and given a single and set-valued operators A : X → X and. The forward-backward splitting method (2) includes the proximal point algorithm, (see, e.g., [8,9,10,11,12]), and the gradient method (see, for example, [2,13]). Several other modifications of (2) with inertial extrapolation step have been considered in Hilbert spaces by many authors, see, for example, [17,18,19,20,21]. We extend the results of [17] concerning the inertial Krasnoselskii–Mann iteration for fixed point of nonexpansive mappings to uniformly convex and q-uniformly smooth Banach space. We extend the forward-backward splitting method with inertial extrapolation step for solving (1) from. While the mentioned results establish only weak convergence, we provide strong convergence analysis in Banach spaces.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
