Applications of measures of weak noncompactness and some classes of operators in the theory of functional equations in the lebesgue space

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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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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Local equivalence of functional equations

Ukrainian Mathematical Journal ◽

10.1007/bf01055959 ◽

1986 ◽

Vol 37 (4) ◽

pp. 406-408

Author(s):

L. P. Kuchko

Keyword(s):

Functional Equations ◽

Local Equivalence

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Wilson's functional equations on groups

Aequationes Mathematicae ◽

10.1007/bf01827944 ◽

1995 ◽

Vol 49 (1) ◽

pp. 252-275 ◽

Cited By ~ 11

Author(s):

Henrik Stetkaer

Keyword(s):

Functional Equations ◽

Functional Equations On Groups

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Gamma Function and Its Functional Equations

Resonance ◽

10.1007/s12045-021-1136-x ◽

2021 ◽

Vol 26 (3) ◽

pp. 367-386

Author(s):

Ritesh Goenka ◽

Gopala Krishna Srinivasan

Keyword(s):

Gamma Function ◽

Functional Equations

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

Demonstratio Mathematica ◽

10.1515/dema-2019-0038 ◽

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.

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Compact Differences of Composition Operators on Bergman Spaces Induced by Doubling Weights

Journal of Geometric Analysis ◽

10.1007/s12220-021-00724-y ◽

2021 ◽

Author(s):

Bin Liu ◽

Jouni Rättyä ◽

Fanglei Wu

Keyword(s):

Bergman Space ◽

Open Problem ◽

Lebesgue Space ◽

Composition Operators ◽

Bergman Spaces ◽

Weighted Bergman Space ◽

Carleson Measures ◽

Doubling Weights ◽

The Way

AbstractBounded and compact differences of two composition operators acting from the weighted Bergman space $$A^p_\omega $$ A ω p to the Lebesgue space $$L^q_\nu $$ L ν q , where $$0<q<p<\infty $$ 0 < q < p < ∞ and $$\omega $$ ω belongs to the class "Equation missing" of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proofs a new description of q-Carleson measures for $$A^p_\omega $$ A ω p , with $$p>q$$ p > q and "Equation missing", involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space $$A^p_\alpha $$ A α p with $$-1<\alpha <\infty $$ - 1 < α < ∞ to the setting of doubling weights. The case "Equation missing" is also briefly discussed and an open problem concerning this case is posed.

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