Abstract
In this work, we investigate the existence of periodic points of mappings defined on nonconvex domains within the variable exponent sequence spaces ℓp(·). In particular, we consider the case of modular firmly nonexpansive and modular firmly asymptotically nonexpansive mappings. These kinds of results have never been obtained before.
Highlights
A central concept in nonlinear analysis and optimization is that of a firmly nonexpansive mapping, mainly due to its relation with maximally monotone operators, as evidenced in [1,2,3,4,5] and the references therein
The definition of firmly nonexpansive mappings on Banach spaces was introduced by Bruck [8] in 1973
We investigate the existence of periodic points for firmly asymptotically nonexpansive mappings defined within the spacesp(·)
Summary
A central concept in nonlinear analysis and optimization is that of a firmly nonexpansive mapping, mainly due to its relation with maximally monotone operators, as evidenced in [1,2,3,4,5] and the references therein. This work delves deeper into firm nonexpansiveness in the modular setting; we recover most of the results by [9] for mappings defined on the variable exponent sequence spacesp(·) . We investigate the existence of periodic points for firmly asymptotically nonexpansive mappings defined within the spacesp(·) . Λ-$-firmly asymptotically nonexpansive if there exists a sequence of positive numbers {k p }
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.
