Common Attractive Points of Generalized Hybrid Multi-Valued Mappings and Applications

In this paper, we first propose the concepts of (ζ,η,λ,π)-generalized hybrid multi-valued mappings, the set of all the common attractive points (CAf,g) and the set of all the common strongly attractive points (CsAf,g), respectively for the multi-valued mappings f and g in a CAT(0) space. Moreover, we give some elementary properties in regard to the sets Af, Ff and CAf,g for the multi-valued mappings f and g in a complete CAT(0) space. Furthermore, we present a weak convergence theorem of common attractive points for two (ζ,η,λ,π)-generalized hybrid multi-valued mappings in the above space by virtue of Banach limits technique and Ishikawa iteration respectively. Finally, we prove strong convergence of a new viscosity approximation method for two (ζ,η,λ,π)-generalized hybrid multi-valued mappings in CAT(0) spaces, which also solves a kind of variational inequality problem.

Generalised Limits for Vector Valued Sequences

The object of the present paper is to introduce the extension of the concept of Banach limits for vector valued sequences and we prove the existence of Banach limits for vector valued sequences. Also introduced Banach spaces X,X^*,X^(**) 1-complemented in their bi duals admit vector valued Banach limits. Lastly we propose Lorentz’s vector valued intrinsic characterisation of almost convergence.