We show that any Lipschitz projection-valued function p on a connected closed Riemannian manifold can be approximated uniformly by smooth projection-valued functions q with Lipschitz constant close to that of p. This answers a question of Rieffel.

Article history: Received 15 April 2016 Received in revised form 27 September 2016 Accepted 5 October 2016 Available online 6 October 2016 In this study, Re-Ni alloys with high Re content were electrodeposited on copper substrates from aqueous solutions containing additives with a combination of vanillin, sodium lauryl sulfate and gelatin. The bath additives were found to have a significant eff...

In recent years, wavelet-based algorithms have been successful in different signal processing tasks. The wavelet transform is a powerful tool because it manages to represent both transient and stationary behaviors of a signal with few transform coefficients. Discontinuities often carry relevant signal information, and therefore, they represent a critical part to analyze. In this paper, we study...

In this paper, we will study concentration inequalities for Banach space-valued martingales. Firstly, prove that a space X is linearly isomorphic to p-uniformly smooth ( $$1<p\le 2$$ ) if and only an Azuma-type inequality holds X-valued This can be viewed as generalization of Pinelis’ work on Azuma martingales with values in 2-uniformly spaces. Secondly, self-normalized sums presented. Finally,...

In this paper, we introduce and study an inertial algorithm for approximating solutions of split equality fixed point problem (SEFPP), involving quasi-phi-nonexpansive mappings in uniformly smooth 2-uniformly convex real Banach spaces establish a strong convergence theorem. We give applications our result to (SEP), variational inclusion (SEVIP) equilibrium (SEEP). Our results extend, generalize...

Let C be a nonempty closed convex subset of a real uniformly smooth Banach space X, {Tk}k 1 : C → C an infinite family of nonexpansive mappings with the nonempty set of common fixed points ⋂∞ k 1 Fix Tk , and f : C → C a contraction. We introduce an explicit iterative algorithm xn 1 αnf xn 1 − αn Lnxn, where Ln ∑n k 1 ωk/sn Tk, Sn ∑n k 1 ωk, and wk > 0 with ∑∞ k 1 ωk 1. Under certain appropriat...

Let B be a real Banach space with the dual space B∗. Let φ : B → R ∪ { ∞} be a proper functional and let Θ : B × B → R be a bifunction. In this paper, a new concept of η-proximal mapping of φ with respect to Θ is introduced. The existence and Lipschitz continuity of the η-proximal mapping of φ with respect to Θ are proved. By using properties of the η-proximal mapping of φ with respect to Θ, a ...

(3) { zn = βnxn + (1− βn)Txn, xn+1 = αnxn + (1− αn)Tzn, n ≥ 0, where the initial guess x0 is taken arbitrarily and {αn}n=0 and {βn} are sequences in the interval [0, 1]. In general not much has been known regarding the convergence of the iteration processes (1)-(3) unless the underlying space X has nice properties which we briefly mention here. The iteration process (1) has been proved to be st...

We consider the numerical approximation of singularly perturbed elliptic problems in smooth domains. The solution to such problems can be decomposed into a smooth part and a boundary layer part. We present guidelines for the eeective resolution of boundary layers in the context of the hp nite element method and we construct tensor product spaces that approximate these layers uniformly at a near...