Stability of the Drygas Functional Equation on Restricted Domain

Piszczek, Magdalena; Szczawińska, Joanna

doi:10.1007/s00025-014-0418-y

Cited by 12 publications

(7 citation statements)

References 9 publications

(10 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(6.4) and (6.5) were applied for the analogous purposes (cf. [8,38,55]); we refer to [12,15,35,49,53,54,71,72,[77][78][79][80]85] for further related information and stability results for those equations.…”

Section: Stability Of Eq (12)mentioning

confidence: 99%

A fixed point theorem and Ulam stability of a general linear functional equation in random normed spaces

Benzarouala

Brzdęk

Oubbi

2022

J. Fixed Point Theory Appl.

View full text Add to dashboard Cite

We prove a very general fixed point theorem in the space of functions taking values in a random normed space (RN-space). Next, we show several of its consequences and, among others, we present applications of it in proving Ulam stability results for the general inhomogeneous linear functional equation with several variables in the class of functions f mapping a vector space X into an RN-space. Particular cases of the equation are for instance the functional equations of Cauchy, Jensen, Jordan–von Neumann, Drygas, Fréchet, Popoviciu, the polynomials, the monomials, the p-Wright affine functions, and several others. We also show how to use the theorem to study the approximate eigenvalues and eigenvectors of some linear operators.

show abstract

Section: Stability Of Eq (12)mentioning

confidence: 99%

A fixed point theorem and Ulam stability of a general linear functional equation in random normed spaces

Benzarouala

Brzdęk

Oubbi

2022

J. Fixed Point Theory Appl.

View full text Add to dashboard Cite

show abstract

“…Piszczek and Szczawińska [22] obtained the stability of the equation (1.2) on a restricted domain. In 2013, Chung [5] investigated the stability of a conditional Cauchy equation on a set of measure zero.…”

Section: Theorem 12 ([16]mentioning

confidence: 99%

Stability of Pexiderized quadratic functional equation on a set of measure zero

EL-Fassi¹,

Chahbi²,

Kabbaj³

et al. 2016

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

show abstract

“…in Banach space, where a, b, A, B = 0 and a + b = A + B, Recently, several mathematicians have investigated the problem of Hyers-Ulam stability of functional equations (see [2,19,20,21,27,30,38,39,42,43,44,47]).…”

mentioning

confidence: 99%

Stability analysis of generalized linear functional equations employing the fixed point approach

Lyu,

liu,

Jin

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

Stability of the Drygas Functional Equation on Restricted Domain

Abstract: Abstract.We study the stability of the Drygas functional equation on a restricted domain. The main tool used in the proofs is the fixed point theorem for functional spaces.Mathematics Subject Classification. 39B82, 47H10, 47J20.

Cited by 12 publications

References 9 publications

A fixed point theorem and Ulam stability of a general linear functional equation in random normed spaces

A fixed point theorem and Ulam stability of a general linear functional equation in random normed spaces

Stability of Pexiderized quadratic functional equation on a set of measure zero

Stability analysis of generalized linear functional equations employing the fixed point approach

Contact Info

Product

Resources

About