Fredholm property of functional equations with affine transformations of argument

This chapter presents some results about groups generated by reflections and the standard metric on a Bruhat-Tits building. It begins with definitions relating to an affine subspace, an affine hyperplane, an affine span, an affine map, and an affine transformation. It then considers a notation stating that the convex closure of a subset a of X is the intersection of all convex sets containing a and another notation that denotes by AGL(X) the group of all affine transformations of X and by Trans(X) the set of all translations of X. It also describes Euclidean spaces and assumes that the real vector space X is of finite dimension n and that d is a Euclidean metric on X. Finally, it discusses Euclidean representations and the standard metric.

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Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

Annals of the Alexandru Ioan Cuza University - Mathematics ◽

10.2478/v10157-012-0047-2 ◽

2013 ◽

Vol 59 (2) ◽

pp. 299-320

Author(s):

M. Eshaghi Gordji ◽

Y.J. Cho ◽

H. Khodaei ◽

M. Ghanifard

Keyword(s):

Functional Equation ◽

General Solution ◽

Functional Equations ◽

Mixed Type ◽

Additive Functional ◽

Normed Spaces ◽

Additive Functional Equation ◽

Probabilistic Normed Spaces ◽

Random Normed Spaces ◽

Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

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An Analog-to-Information Approach Using Adaptive Compressive Sampling and Nonlinear Affine Transformations. Analog-to-Information GMR-UW Collaboration

10.21236/ada482017 ◽

2008 ◽

Author(s):

Gil M. Raz ◽

Robert D. Nowak

Keyword(s):

Compressive Sampling ◽

Affine Transformations ◽

Information Approach

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An Empirical Evaluation of the Estimation of Affine Term Structure Models: How Invariant Affine Transformations and Rotations Lead to Improved Empirical Performance

SSRN Electronic Journal ◽

10.2139/ssrn.1361050 ◽

2009 ◽

Author(s):

Januj Juneja

Keyword(s):

Term Structure ◽

Empirical Evaluation ◽

Affine Transformations ◽

Affine Term Structure ◽

Affine Term Structure Models ◽

Term Structure Models ◽

Empirical Performance

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Identities related to special polynomials and combinatorial numbers

Filomat ◽

10.2298/fil1715833y ◽

2017 ◽

Vol 31 (15) ◽

pp. 4833-4844 ◽

Cited By ~ 2

Author(s):

Eda Yuluklu ◽

Yilmaz Simsek ◽

Takao Komatsu

Keyword(s):

Generating Functions ◽

Functional Equations ◽

Stirling Numbers ◽

Bernoulli Numbers ◽

Euler Numbers ◽

Special Polynomials ◽

Central Factorial Numbers

The aim of this paper is to give some new identities and relations related to the some families of special numbers such as the Bernoulli numbers, the Euler numbers, the Stirling numbers of the first and second kinds, the central factorial numbers and also the numbers y1(n,k,?) and y2(n,k,?) which are given Simsek [31]. Our method is related to the functional equations of the generating functions and the fermionic and bosonic p-adic Volkenborn integral on Zp. Finally, we give remarks and comments on our results.

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