On the Fixed Point Property for Nonexpansive Mappings on Large Classes in α-duals of Certain Difference Sequence Spaces

Abstract

In 2000, Et and Esi introduced new type of generalized difference sequences by using the structure of Çolak’s work from 1989 where he defined new types of sequence spaces while Çolak was also inspired by Kızmaz’s idea about the difference operator he studied in 1981. Then, using Et and Esi’s structure, Ansari and Chaudhry, in 2012, introduced a new type of generalized difference sequence spaces. Changing Ansari and Chaudhry’s construction slightly, Et and Işık, in 2012, obtained new type of generalized difference sequence spaces which have equivalent norm to that of Ansari and Chaudhry’s type Banach spaces. Then, Et and Işık found α-duals of the Banach spaces they got and investigated geometric properties for them. In this study, we consider Et and Işık’s work and study α-duals of their generalized difference sequence spaces. We take their study in terms of fixed point theory and find large classes of closed, bounded and convex subsets in those duals with fixed point property for nonexpansive mappings.

Keywords

• Nonexpansive Mapping
• Fixed Point Property
• Closed Bounded Convex Set
• Difference Sequences
• α-duals

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