We prove common fixed point theorems in symmetric spaces for two pairs of hybrid mappings using the concept of T−weakly and S−weakly commuting mappings satisfying generalized contractive conditions which generalize theorems of Aamri and El Moutawakil [J. Math. Anal. Appl., 270 (2002), 181–188.], Aamri and El Moutawakil [Appl. Math. E-notes., 3 (2003), 156–162.] and Aliouche [J. Math. Anal. Appl...

In the last years, fixed point theorems have been applied to show the existence and uniqueness of the solutions of differential equations, integral equations and many other branches mathematics see, e.g., 1–3 . Some common fixed point theorems for weakly commuting, compatible, δ-compatible and weakly compatible mappings under different contractive conditions in metric spaces have appeared in 4–...

Let X be a reflexive Banach space which has a weakly sequentially continuous duality mapping. In this paper, we consider the following viscosity approximation sequence x n λ n fx n 1−λ n T n x n , where λ n ∈ 0, 1, {T n } is a uniformly asymptotically regular sequence, and f is a weakly contractive mapping. Strong convergence of the sequence {x n } is proved.

Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, non-expansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which ...

Let $T\colon L^p({\mathcal M})\to N})$ be a bounded operator between two noncommutative $L^p$-spaces, $1\leq p<\infty$. We say that $T$ is $\ell^1$-bounded (resp. $\ell^1$-contractive) if $T\otimes I_{\ell^1}$ extends to contractive) map from $L^p({\mathcal M};\ell^1)$ into N};\ell^1)$. show Yeadon's factorization theorem for $L^p$-isometries, p\not=2 <\infty$, applies an isometry L^2({\mathcal...

Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, nonexpansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which a...