Some Fixed Point Results for a New Multivalued Hybrid Mapping in Geodesic Spaces

Emirhan Hacıoğlu, Vatan Karakaya

Abstract

The studies about hybrid mappings are mainly focused for single-valued mappings in Hilbert spaces. We define a new class of multivalued mappings in CAT ($\kappa$) spaces which contains the multivalued nonexpansive mappings, $\alpha$-nonexpansive mappings and some hybrid mappings such as $(\alpha, \beta)$-hybrid mappings and we study existence and convergence of this new class of mappings on CAT($\kappa$) spaces which is more general than CAT(0) spaces and also non-Euclidean generalization of Hilbert spaces.