The propose of this paper is to present a modified block iterative algorithm for finding a common element between the set of solutions of the fixed points of two countable families of asymptotically relatively nonexpansive mappings and the set of solution of the system of generalized mixed equilibrium problems in a uniformly smooth and uniformly convex Banach space. Our results extend many know...

Let A be a C*-algebra. Let z be the maximal atomic projection in A∗∗. By a theorem of Brown, x in A∗∗ has a continuous atomic part, i.e. zx = za for some a in A, whenever x is uniformly continuous on the set of pure states of A. Let L be a closed left ideal of A. Under some additional conditions, we shall show that for any x in A∗∗, x has a continuous atomic part modulo L∗∗, i.e. zx + L∗∗ = za ...

It is shown that the bilinear Hilbert transforms Hα,β(f, g)(x) = p.v. Z R f(x− αt)g(x− βt) dt t map L1(R)×L2(R)→ L(R) uniformly in the real parameters α, β when 2 < p1, p2 <∞ and 1 < p = p1p2 p1+p2 < 2. Combining this result with the main result in [9], it follows that the operators H1,α map L (R) × L∞(R) → L(R) uniformly in the real parameter α ∈ [0, 1], as conjectured by A. Calderón.

We propose to extend Talenti’s estimates on the L norm of the second order derivatives of the solutions of a uniformly elliptic PDE with measurable coefficients satisfying the Cordes condition to the non-uniformly elliptic case.

in this paper we introduce the notions of uniformly quasi-primary ideals and uniformly classical quasi-primary submodules that generalize the concepts of uniformly primary ideals and uniformly classical primary submodules; respectively. several characterizations of classical quasi-primary and uniformly classical quasi-primary submodules are given. then we investigate for a ring $r$, when any fi...

Let  $left{a_alpharight}_{alphain I}$ be a bounded net in a Banach algebra $A$ and $varphi$ a nonzero multiplicative linear functional on $A$. In this paper, we deal with the problem of when $|aa_alpha-varphi(a)a_alpha|to0$ uniformly for all $a$ in weakly compact subsets of $A$. We show that Banach algebras associated to locally compact groups such  as Segal algebras and $L^1$-algebras are resp...

Let { n} be a system of monic polynomials orthogonal on the unit circle with respect to a positive Borel measure p.. It is shown that under .fairly mild conditions on the reflection coefficients, n(O), the zeros of a subsequence of { n} are asymptotically uniformly distributed on some circle. The radius of this circle can be found using a Cauchy-Hadamard-type formula. We also character...

in this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $x$,  where $x$ is a $c$-distinguished topological space. then, we show that their dual spaces can be identified in a natural way with certain spaces of radon measures.

In this paper, we show that the modified Mann iteration with errors converges strongly to fixed point for uniformly L-Lipschitzian asymptotically Φ-pseudocontractive mappings in real Banach spaces. Meanwhile, it is proved that the convergence of Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitzian asymptotically Φpseudocontractive mappings in real Banach spaces. Finally, we o...