Abstract
In this paper, a new modified Ishikawa iterative algorithm with errors by a shrinking projection method for generalized mixed equilibrium problems and a countable family of uniformly Bregman totally quasi-D-asymptotically nonexpansive mappings is introduced and investigated in the framework of a real Banach space. Strong convergence of the sequence generated by the proposed algorithm is derived under some suitable assumptions. These results are new and develop some recent results in this field.
Highlights
Introduction and preliminariesIn this paper, without other specifications, let N∗ and R be the sets of positive integers and real numbers, respectively, C be a nonempty, closed, and convex subset of a real Banach space E with the dual space E∗
Chen et al [ ] introduced the concept of weak Bregman relatively nonexpansive mappings in a reflexive Banach space and gave an example to illustrate the existence of a weak Bregman relatively nonexpansive mapping and the difference between a weak Bregman relatively nonexpansive mapping and a Bregman relatively nonexpansive mapping
Motivated by the above mentioned results and the on-going research, in this paper, using Bregman function and the shrinking projection method, we introduce new modified Ishikawa iterative algorithms with errors for finding a common element of solutions to the generalized mixed equilibrium problems ( . ) and fixed points to a countable family of Bregman totally quasi-D-asymptotically nonexpansive mappings in Banach spaces
Summary
Without other specifications, let N∗ and R be the sets of positive integers and real numbers, respectively, C be a nonempty, closed, and convex subset of a real Banach space E with the dual space E∗. The norm and the dual pair between E∗ and E are denoted by · and ·, · , respectively. Let g : E → R ∪ {+∞} be a proper convex and lower semicontinuous function. The Fenchel conjugate of g is the function g∗ : E∗ → (–∞, +∞] defined by g∗(ζ ) = supx∈E{ ζ , x – g(x)}. Let T : E → C be a nonlinear mapping. Let {xn} be a sequence in E, we denote the strong convergence of {xn} to x ∈ E by xn → x. For any x ∈ int(dom g), the right-hand derivative of g at x in the direction y ∈ E is defined by g
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.
