ALGORITHMS FOR APPROXIMATING FIXED POINTS OF MULTIVALUED QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES
ABSTRACT
The abstract summarizes a mathematical study conducted in the field of functional analysis. Here is the abstract rewritten for clarity:
In this study, we consider a strictly convex real Banach space E and a non-empty closed convex subset D ⊆ E. We examine a finite family {T}i∈I of multivalued maps that are quasi-nonexpansive and continuous with respect to the Hausdorff metric. Each map Ti : D −→ PB(D) is defined on the subset D and takes values in the power set of D, for all i ∈ I. We assume that the family of maps has at least one common fixed point.
Using a Krasnolselskii-Mann-type sequence, we demonstrate that the sequence converges strongly to a common fixed point of the maps Ti. This result extends and complements previous findings on both single-valued and multivalued quasi-nonexpansive maps.
Furthermore, we extend our analysis to include a countable family of quasi-nonexpansive multivalued maps and establish a similar convergence result.
In summary, this study explores the convergence properties of a family of quasi-nonexpansive multivalued maps in a strictly convex real Banach space. The results obtained generalize and complement existing findings and provide insights into the behavior of such maps.
ALGORITHMS FOR APPROXIMATING FIXED POINTS OF MULTIVALUED QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES. GET MORE MATHEMATICS PROJECT TOPICS AND MATERIALS DOC & PDF