Common fixed points of monotone ρ-nonexpansive semigroup in modular 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...

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...

On common approximate fixed points of monotone nonexpansive semigroups in Banach spaces

*Correspondence: [email protected] 1Department of Mathematics, College of Sciences, King Saud University, Riyadh, Saudi Arabia Full list of author information is available at the end of the article Abstract In this paper, we investigate the common approximate fixed points of monotone nonexpansive semigroups of nonlinear mappings {T (t)}t≥0, i.e., a family such that T (0)x = x, T (s + t)x = T (...

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...

Common Fixed Point Theorems of Integral Type in Modular Spaces