Viscosity Approximation Methods for <inline-formula> <mml:math id="mm1000" display="block"> <mml:semantics> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:semantics> </mml:math> </inline-formula>−Nonexpansive Multi-Valued Mappings in Convex Metric Spaces

• Main Authors: Azadeh Ghanifard, Hashem Parvaneh Masiha, Manuel De La Sen, Maryam Ramezani
• Format: Article
• Language: English
• Published: MDPI AG 2020-01-01
• Series: Axioms
• Subjects: *−nonexpansive multi-valued mapping; viscosity approximation methods; fixed point; convex metric space
• Online Access: https://www.mdpi.com/2075-1680/9/1/10
• ISSN: 2075-1680

In this paper, we prove convergence theorems for viscosity approximation processes involving <inline-formula> <math display="inline"> <semantics> <mrow> <mo>*</mo> </mrow> </semantics> </math> </inline-formula>&#8722;nonexpansive multi-valued mappings in complete convex metric spaces. We also consider finite and infinite families of such mappings and prove convergence of the proposed iteration schemes to common fixed points of them. Our results improve and extend some corresponding results.