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 }
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