This paper is devoted to the study of orthogonality and disjointness preserving linear maps between Fourier and FourierStieltjes algebras of locally compact groups. We show that a linear bijection : A (G 1) A (G 2)(resp. : B (G 1) B (G 2)) between two Fourier algebras (resp. FourierStieltjes algebras) of locally compact groups will induce a topological group isomorphism between G 1 and G 2, provided that preserves both disjointness and some kind of orthogonality. This improves earlier results of JJ Font and MS Monfared, where amenability of the groups or continuity of the linear maps are assumed. We also study the structure of bounded and unbounded disjointness preserving linear functionals of Fourier algebras. In the development, general results about disjointness and orthogonality preserving linear maps between C-algebras, W-algebras and their preduals are obtained.

Let <i>X</i> be a locally compact Hausdorff space and <i>C</i> ₀(<i>X</i>) the Banach space of continuous functions on <i>X</i> vanishing at infinity. In this paper, we shall study unbounded disjointness preserving linear functionals on <i>C</i> ₀(<i>X</i>). They arise from prime ideals of <i>C</i> ₀(<i>X</i>), and we translate it into the cozero set ideal setting. In particular, every unbounded disjointness preserving linear functional of <i>c</i> ₀ can be constructed explicitly through an ultrafilter on complementary to a cozero set ideal. This ultrafilter method can be extended to produce many, but in general not all, such functionals on <i>C</i> ₀(<i>X</i>) for arbitrary <i>X</i>. We also make some remarks where <i>C</i> ₀(<i>X</i>) is replaced by a non-commutative C*-algebra.

We study the following generalized quasivariational inequality problem: given a closed convex set <i>X</i> in a normed space <i>E</i> with the dual <i>E</i> ^*, a multifunction \Phi :Xightarrow 2^{E^{*}} and a multifunction :<i>X</i>2^<i>X</i>, find a point \Phi :Xightarrow 2^{E^{*}} such that \Phi :Xightarrow 2^{E^{*}} , \Phi :Xightarrow 2^{E^{*}} . We prove some existence theorems in which may be discontinuous, <i>X</i> may be unbounded, and is not assumed to be Hausdorff lower semicontinuous.

Let E be a real Banach space with a uniformly Gteaux differentiable norm and which possesses uniform normal structure, K a nonempty bounded closed convex subset of E,{T i} i= 1 N a finite family of asymptotically nonexpansive self-mappings on K with common sequence {k n} n= 1[1,),{t n},{s n} be two sequences in (0, 1) such that s n+ t n= 1 (n 1) and f be a contraction on K. Under suitable conditions on the sequences {s n},{t n}, we show the existence of a sequence {x n} satisfying the relation x n=(1 1 k n) x n+ s n k n f (x n)+ t n k n T r n n x n where n= l n N+ r n for some unique integers l n 0 and 1 r n N. Further we prove that {x n} converges strongly to a common fixed point of {T i} i= 1 N, which solves some variational inequality, provided x n T i x n 0 as n for i= 1, 2,, N. As an application, we prove that the iterative process defined by z 0 K, z n+ 1=(1 1 k n) z n+ s n k n f (z n)+ t n k n

Let and be a real uniformly smooth Banach space. Let be a nonempty closed convex subset of and be a strictly pseudocontractive mapping in the sense of FE Browder and WV Petryshyn [1]. Let be a bounded sequence in and be real sequences in satisfying some restrictions. Let be the bounded sequence in generated from any given by the Ishikawa iteration method with errors: , , . It is shown in this paper that if is compact or demicompact, then converges strongly to a fixed point of .