In this paper, we introduce a new type of a projective algorithm for a pair of quasi-φ-nonexpansive mappings. We establish strong convergence theorems of common fixed points in uniformly smooth and strictly convex Banach spaces with the property(K). Our results improve and extend the corresponding results announced by many others. AMS subject classifications: 47H09, 47H10

This paper discusses the existence and decay of solutions u(t) of the variational inequality of parabolic type: >_ 0 for v e LP([O,=);V (p>2) with v(t) e K a.e. in [0,=), where K is a closed convex set of a separable uniformly convex Banach space V, A is a nonlinear monotone operator from V to V* and B is a nonlinear operator from Banach space W to W*. V ...

We give a characterization of uniformly convex Banach spaces in terms of a uniform version of the Kadec-Klee property. As an application we prove that if (xn) is a bounded sequence in a uniformly convex Banach space X which is ε-separated for some 0 < ε ≤ 2, then for all norm one vectors x ∈ X there exists a subsequence (xn j) of (xn) such that inf j =k x − (xn j − xn k) ≥ 1 + δ X (2 3 ε), wher...

In this paper we show the weak Banach-Saks property of the Banach vector space (L p µ) m generated by m L p µ-spaces for 1 ≤ p < +∞, where m is any given natural number. When m = 1, this is the famous Banach-Saks-Szlenk theorem. By use of this property, we also present inequalities for integrals of functions that are the composition of nonnegative continuous convex functions on a convex set of ...

In this paper, we unify the theory of SSD spaces, part of the theory of strongly representable multifunctions, and the theory of the equivalence of various classes of maximally monotone multifunctions. 0 Introduction In this paper, we unify three different lines of investigation: the theory of SSD spaces as expounded in [11] and [13], part of the theory of strongly representable multifunctions ...

This article gives dual representations for convex integral functionals on the linear space of regular processes. This space turns out to be a Banach space containing many more familiar classes of stochastic processes and its dual is identified with the space of optional Radon measures with essentially bounded variation. Combined with classical Banach space techniques, our results allow for sys...

We completely characterize extreme contractions between two-dimensional strictly convex and smooth real Banach spaces, perhaps for the very first time. In order to obtain desired characterization, we introduce notions of (weakly) compatible point pair (CPP) μ-compatible (μ-CPP) in geometry spaces. As a concrete application our abstract results, describe all rank one L(ℓ42,ℓ42) L(ℓ42,H), where H...