Let E be a real Banach space with norm ∥.∥ and let J be the normalized duality mapping from E into 2E ∗ given by Jx = {x∗ ∈ E∗ : ⟨x, x∗⟩ = ∥x∥∥x∗∥, ∥x∥ = ∥x∗∥} for all x ∈ E, where E∗ denotes the dual space of E and ⟨., .⟩ denotes the generalized duality pairing between E and E∗. A Banach space E is said to be strictly convex if ∥ 2 ∥ < 1 for all x, y ∈ E with ∥x∥ = ∥y∥ = 1 and x ̸= y. It is sai...

and Applied Analysis 3 Lemma 1 (see [1, 2]). Let E be a Banach space and let J be the normalized duality mapping on E. Then for any x, y ∈ E, the following inequality holds: 󵄩󵄩󵄩󵄩x + y 󵄩󵄩󵄩󵄩 2 ≤ ‖x‖ 2 + 2⟨y, j (x + y)⟩, ∀j (x + y) ∈ J (x + y) . (14) Lemma 2 (see [20]). Let {s n } be a sequence of nonnegative real numbers satisfying s n+1 ≤ (1 − λ n ) s n + λ n δ n , ∀n ≥ 0, (15) where {λ n } and ...

Introducing the concept of the normalized duality mapping on normed linear space and normed algebra, we extend the usual definitions of the numerical range from one operator to two operators. In this note we study the convexity of these types of numerical ranges in normed algebras and linear spaces. We establish some Birkhoff-James orthogonality results in terms of the algebra numerical range V...

Abstract The purpose of this paper is to give a regularization variant of the inertial proximal point algorithm not only in an infinite-dimensional Banach space E, which is an uniformly smooth and uniformly convex, but also in its finite-dimensional approximations for finding a point in the nonempty intersection ∩i=1Ci, where N ≥ 1 is an integer and each Ci is assumed to be the fixed point set ...

In this paper we propose and studied a new composite iterative scheme with certain control con-ditions for viscosity approximation for a zero of accretive operator and xed points problems in areflexive Banach space with weakly continuous duality mapping. Strong convergence of the sequencefxng dened by the new introduced iterative sequence is proved. The main results improve andcomplement the co...

LetK be a nonempty closed convex subset of a real Banach space E, T : K → K a uniformly L-Lipschitzian asymptotically pseudocontractive mapping with sequence {kn}n≥0 ⊂ [1,∞), lim n→∞ kn = 1 such that p ∈ F (T ) = {x ∈ K : Tx = x}. Let {an}n≥0, {bn}n≥0 , {cn}n≥0 be real sequences in [0, 1] satisfying the following conditions: (i) an + bn + cn = 1; (ii) ∑ n≥0 bn =∞; (iii) cn = o(bn); (iv) lim n→∞...

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...

Identification of materials based on spectral reflectance is confounded by variations in magnitude that are independent the shape. Local such as viewing/illumination angles, multiscale soil surface roughness causes shadows and redistributes light, moisture content, all drive changes distinct from variations, complicate identification modeling targets features. Normalization metrics remove can g...