[PDF] Top 20 Approximation of Functions by Quadratic Mapping in (β, p) Banach Space

... Now we recall some basic facts concerning ( β , p ) -Banach spaces. We fixed real numbers β with 0 < ≤ β 1 and p with 0 < ≤ p 1 . Let  =  or  . Let X be linear space over  . A quasi- β -norm ⋅ is ... See full document

... reflexive Banach space E, and let J be the duality mapping from E into E ∗ such that J(C) is closed and convex, let us assume that a bifunction F : J(C) × J(C) → R satisfies the following conditions ... See full document

... in Banach spaces can be found in Kopeck´a and Reich ...A Banach space is said to admit a weakly sequentially con- tinuous normalized duality mapping J, if J : E → E ∗ is single-valued and ... See full document

... Theorem 2.1. [4] (Arzela-Ascoli Theorem) If every uniformly bounded and equi - continuous sequence =( O ? of functions in ,ℝ , ℝ , then it has a convergent subsequence. Theorem 2.2. [4] A metric space X is ... See full document

... monotone mapping Q is said to be maximal iff its graph Graph(Q) = { (x, f ) : f ∈ Qx } is not properly contained in the graph of any other monotone ...monotone mapping Q is maximal iff for (x, f ) ∈ E × E ∗ , ... See full document

... multi-Banach space. Suppose that m ∈ N and f : E → F is a mapping satisfying f (0) = 0 for which there exists a control function ϕ : E nm → [0, ∞) satisfying ... See full document

... real Banach E , { S i : C → C , i = 1 , 2 , … , k } a family of generalized asymptotically quasi-nonexpansive mappings and f : C → C a fixed contractive mapping with contractive coefficient α ∈ [ 0 , 1 ] ... See full document

... In 1821, it was first solved by A.L. Cauchy in the class of continuous real-valued functions. It is often called an additive Cauchy functional equation in honour of Cauchy .The theory of additive functional ... See full document

... the quadratic functional equation ...the functions f E : 1  E 2 where E 1 is the normed space and E 2 be a Banach space, the result of Skof is still true if the relevant domain ... See full document

... Hyers 2 proved the stability problem of additive mappings in Banach spaces. Rassias 3 provided a generalization of Hyers theorem which allows the Cauchy difference to be unbounded: let f : E → E be a mapping ... See full document

... f x  y  f x  f y , x  y , where  is the orthogonality symbol was investigated by S. Gudder and D. Strawther [21]. Later on, Ger and Sikorska [19] established the orthogonal stability of above additive functional ... See full document

... convex Banach space which admits a weakly sequentially continuous duality mapping J from X to X ∗ and C a nonempty closed convex subset of ...nonexpansive mapping, FT / ∅ and f : C → C is a ... See full document

... nonexpansive mapping, which includes a firmly nonexpansive mapping as a special case in a uniformly convex Banach ...reflexive Banach space has the fixed point property for ψ -firmly ... See full document

... These are extensions of Banach contraction principle [1] in terms of a new symmetric rational expression. Recently many other mathematicians viz. Dubey and Pathak [8], Murthy and Sharma [19], Rani and Chug [23] ... See full document

... ( ) . ( ) ( ) . , ( ) . D ab = a D b + D a b a b ∈ A We define δ x ( ) a = . a x − x a . for each x ∈ X and a ∈ A is a derivation from A into X , which is called an inner derivation. A Banach algebra A is amenable ... See full document

... references therein, the continuity (even Lipschitz continuity) of f (or g , h) of two variables is always required. In this paper, we study a more complicated model than previous ones [–], apply different techniques ... See full document

... and ψ(t) =   t. Clearly, (X, d) is a complete metric space. We show that f is a triangular α-admissible mapping. Let x, y ∈ X, if α(x, y) ≥  then x, y ∈ [, ]. On the other hand, for all x, y ∈ [, ] ... See full document

... Keywords: generalized Lipschitz mapping; -hemi-contractive mapping; Ishikawa iterative sequence with errors; uniformly smooth real Banach space.. 1 Introduction and preliminary.[r] ... See full document

... We prove that W"’’gP,E has the approximation property provided E has it, furthermore ifE is a Banach space with the strict approximation property then W’’’R’,E has this property... KEY W[r] ... See full document

... by Banach, called the Banach contraction mapping principle: Every contraction in a complete metric space has a unique fixed ...fact, Banach demonstrated how to find the desired fixed ... See full document