As well known, the Moreau-Rockafellar-Robinson internal point qualification condition is sufficient to ensure that the infimal convolution of the conjugates of two extended-real-valued convex lower semi-continuous functions defined on a locally convex space is exact, and that the sub-differential of the sum of these functions is the sum of their sub-differentials. This note is devoted to provin...

As well known, the Moreau-Rockafellar-Robinson internal point qualification condition is sufficient to ensure that the infimal convolution of the conjugates of two extended-real-valued convex lower semi-continuous functions defined on a locally convex space is exact, and that the subdifferential of the sum of these functions is the sum of their subdifferentials. This note is devoted to proving ...

begin{abstract} in this paper, we prove some strong and weak convergence of three step random iterative scheme with errors to common random fixed points of three asymptotically nonexpansive nonself random mappings in a real uniformly convex separable banach space. end{abstract}

in this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex banach space. we establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.

This paper concerns the dynamics of non-expansive maps on strictly convex finite dimensional normed spaces. By using results of Edelstein and Lyubich, we show that if X = (R, ‖ · ‖) is strictly convex and X has no 1-complemented Euclidean plane, then every bounded orbit of a non-expansive map f : X → X , converges to a periodic orbit. By putting extra assumptions on the derivatives of the norm,...

Maximal monotone operators on a Banach space into its dual can be represented by convex functions bounded below by the duality product. It is natural to ask under which conditions a convex function represents a maximal monotone operator. A satisfactory answer, in the context of reflexive Banach spaces, has been obtained some years ago. Recently, a partial result on non-reflexive Banach spaces w...

Some algorithms for nding common xed point of a family of mappings isconstructed. Indeed, let C be a nonempty closed convex subset of a uniformlyconvex Banach space X whose norm is Gateaux dierentiable and let {Tn} bea family of self-mappings on C such that the set of all common fixed pointsof {Tn} is nonempty. We construct a sequence {xn} generated by the hybridmethod and also we give the cond...

If X is a Banach space then the Banach space c(X) of all X-valued convergent sequences contains a nonvoid bounded closed convex body V such that no point in C(X) \ V has a nearest point in V .

This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.