scholarly journals A C0-Semigroup of Ulam Unstable Operators

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1844
Author(s):  
Ana Maria Acu ◽  
Ioan Raşa
Keyword(s):  
Infinitesimal Generator ◽  
Ulam Stability ◽  
Central Moments ◽  
Type Formula ◽  
C0 Semigroup

The Ulam stability of the composition of two Ulam stable operators has been investigated by several authors. Composition of operators is a key concept when speaking about C0-semigroups. Examples of C0-semigroups formed with Ulam stable operators are known. In this paper, we construct a C0-semigroup (Rt)t≥0 on C[0,1] such that for each t>0, Rt is Ulam unstable. Moreover, we compute the central moments of Rt and establish a Voronovskaja-type formula. This enables to prove that C2[0,1] is contained in the domain D(A) of the infinitesimal generator of the semigroup. We raise the problem to fully characterize the domain D(A).

scholarly journals Dua Formula Eksponensial (Operator Linear dari Semigrup)

2021 ◽  
Vol 18 (1) ◽  
pp. 41-46
Author(s):  
L Meisaroh
Keyword(s):  
Linear Operator ◽  
Bounded Linear Operator ◽  
Infinitesimal Generator ◽  
The Other ◽  
Bounded Linear ◽  
Unbounded Linear Operator ◽  
C0 Semigroup

Assumed A is infinitesimal generator of C0-semigroup T(t) on X. This could be defined as T(t)=etA, applies if A is a bounded linear operator. Not if A is unbounded linear operator, then it will result in one possibility that show T(t) could be represented as etA. This paper will discuss and detail the proof of the other two formulas that show T(t) could be represented as etA.

On the stability of a nonic functional equation in quasi-normed spaces

2016 ◽  
Vol 12 (3) ◽  
pp. 4368-4374
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability

In this paper, we extend normed spaces to quasi-normed spaces and prove the generalized Hyers-Ulam stability of a nonic functional equation:$$\aligned&f(x+5y) - 9f(x+4y) + 36f(x+3y) - 84f(x+2y) + 126f(x+y) - 126f(x)\\&\qquad + 84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9 ! f(y),\endaligned$$where $9 ! = 362880$ in quasi-normed spaces.

scholarly journals Verlinde formulae on complex surfaces: K-theoretic invariants

2021 ◽  
Vol 9 ◽  
Author(s):  
L. Göttsche ◽  
M. Kool ◽  
R. A. Williams
Keyword(s):  
Moduli Space ◽  
K3 Surfaces ◽  
Complex Surfaces ◽  
Type Formula ◽  
Verlinde Formula ◽  
Donaldson Invariants

Abstract We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between K-theoretic Donaldson invariants studied by Göttsche and Nakajima-Yoshioka and K-theoretic Vafa-Witten invariants introduced by Thomas and also studied by Göttsche and Kool. We verify our conjectures in many examples (for example, on K3 surfaces).

scholarly journals Hyers-Ulam stability of quadratic forms in 2-normed spaces

2019 ◽  
Vol 52 (1) ◽  
pp. 496-502
Author(s):  
Won-Gil Park ◽  
Jae-Hyeong Bae
Keyword(s):  
Banach Spaces ◽  
Quadratic Forms ◽  
Functional Equations ◽  
Ulam Stability ◽  
Normed Spaces

AbstractIn this paper, we obtain Hyers-Ulam stability of the functional equationsf (x + y, z + w) + f (x − y, z − w) = 2f (x, z) + 2f (y, w),f (x + y, z − w) + f (x − y, z + w) = 2f (x, z) + 2f (y, w)andf (x + y, z − w) + f (x − y, z + w) = 2f (x, z) − 2f (y, w)in 2-Banach spaces. The quadratic forms ax2 + bxy + cy2, ax2 + by2 and axy are solutions of the above functional equations, respectively.

scholarly journals Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Murali Ramdoss ◽  
Divyakumari Pachaiyappan ◽  
Choonkil Park ◽  
Jung Rye Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Research Paper ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Modular Spaces

AbstractThis research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.

scholarly journals Fully degenerate Bell polynomials associated with degenerate Poisson random variables

2021 ◽  
Vol 19 (1) ◽  
pp. 284-296
Author(s):  
Hye Kyung Kim
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Combinatorial Identities ◽  
Bell Polynomials ◽  
Poisson Random Variable ◽  
Central Moments ◽  
Special Polynomials ◽  
Special Numbers And Polynomials ◽  
New Type ◽  
Two Parameters

Abstract Many mathematicians have studied degenerate versions of quite a few special polynomials and numbers since Carlitz’s work (Utilitas Math. 15 (1979), 51–88). Recently, Kim et al. studied the degenerate gamma random variables, discrete degenerate random variables and two-variable degenerate Bell polynomials associated with Poisson degenerate central moments, etc. This paper is divided into two parts. In the first part, we introduce a new type of degenerate Bell polynomials associated with degenerate Poisson random variables with parameter α > 0 \alpha \hspace{-0.15em}\gt \hspace{-0.15em}0 , called the fully degenerate Bell polynomials. We derive some combinatorial identities for the fully degenerate Bell polynomials related to the n n th moment of the degenerate Poisson random variable, special numbers and polynomials. In the second part, we consider the fully degenerate Bell polynomials associated with degenerate Poisson random variables with two parameters α > 0 \alpha \gt 0 and β > 0 \beta \hspace{-0.15em}\gt \hspace{-0.15em}0 , called the two-variable fully degenerate Bell polynomials. We show their connection with the degenerate Poisson central moments, special numbers and polynomials.

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