Approximating fixed points of multivalued ρ-nonexpansive mappings in modular function spaces

Approximating fixed points of multivalued ρ-nonexpansive mappings in modular function spaces

*Correspondence: [email protected]; [email protected] 1Department of Mathematics, Statistics and Physics, Qatar University, Doha, 2713, Qatar Full list of author information is available at the end of the article Abstract The existence of fixed points of single-valued mappings in modular function spaces has been studied by many authors. The approximation of fixed points in such spaces via...

Approximating fixed points of generalized nonexpansive mappings

Convergence of approximating fixed points sets for multivalued nonexpansive mappings

Let K be a closed convex subset of a Hilbert space H and T : K ⊸ K a nonexpansive multivalued map with a unique fixed point z such that {z} = T (z). It is shown that we can construct a sequence of approximating fixed points sets converging in the sense of Mosco to z.

Fixed points of multivalued nonexpansive mappings in Banach spaces

* Correspondence: [email protected] Department of Mathematics, Ataturk University, Erzurum 25240, Turkey Full list of author information is available at the end of the article Abstract In this article, we first give a multivalued version of an iteration scheme of Agarwal et al. We use an idea due to Shahzad and Zegeye which removes a “strong condition” on the mapping involved in the ite...

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...