Fixed Points of Asymptotic Pointwise Nonexpansive Mappings in Modular Spaces

Fixed Points of Asymptotic Pointwise Nonexpansive Mappings in Modular Spaces

The theory of modular spaces was initiated by Nakano 1 in 1950 in connection with the theory of order spaces and redefined and generalized by Musielak and Orlicz 2 in 1959. These spaces were developed following the successful theory of Orlicz spaces, which replaces the particular, integral form of the nonlinear functional, which controls the growth of members of the space, by an abstractly give...

Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces

Let C be a nonempty bounded closed convex subset of a complete CAT 0 space X. We prove that the common fixed point set of any commuting family of asymptotic pointwise nonexpansive mappings on C is nonempty closed and convex. We also show that, under some suitable conditions, the sequence {xk}k 1 defined by xk 1 1 − tmk xk ⊕ tmkT nk m y m−1 k, y m−1 k 1 − t m−1 k xk ⊕ t m−1 kT m−1y m−2 k, y m−2 ...

On fixed points of fundamentally nonexpansive mappings in Banach spaces

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

Approximating fixed points of generalized nonexpansive mappings

on fixed points of fundamentally nonexpansive mappings in banach spaces

we first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a banach space and next show that if the banach space is having the opial condition, then the fixed points set of such a mapping with the convex range is nonempty. in particular, we establish that if the banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...