Results 41 to 50 of about 439,454 (357)
The stability of quadratic-reciprocal functional equation [PDF]
AIP Conference Proceedings, 2018 A new quadratic-reciprocal functional equation f((k+1)x+ky)+f((k+1)x−ky)=2f(x)f(y)[(k+1)2f(y)+k2f(x)][(k+1)2f(y)−k2f(x)]2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.A new quadratic-reciprocal functional equation f ...
Aimin Song, Minwei Song
openaire +2 more sources
Mathematics, 2019 The general quintic functional equation and the general sextic functional equation are generalizations of many functional equations such as the additive function equation and the quadratic function equation. In this paper, we investigate Hyers−Ulam&
Yang-Hi Lee
doaj +1 more source
On the Stability of Quadratic Functional Equations in F-Spaces
Journal of Function Spaces, 2016 The Hyers-Ulam-Rassias stability of quadratic functional equation f(2x+y)+f(2x-y)=f(x+y)+f(x-y)+6f(x) and orthogonal stability of the Pexiderized quadratic functional equation f(x+y)+f(x-y)=2g(x)+2h(y) in F-spaces are proved.
Xiuzhong Yang
doaj +1 more source
Archimedean theory and $\epsilon$-factors for the Asai Rankin-Selberg integrals
, 2020 In this paper, we partially complete the local Rankin-Selberg theory of Asai $L$-functions and $\epsilon$-factors as introduced by Flicker and Kable. In particular, we establish the relevant local functional equation at Archimedean places and prove the ...
Beuzart-Plessis, Raphaël
core +2 more sources
Stability of quadratic functional equations in generalized functions [PDF]
Advances in Difference Equations, 2013 In this paper, we consider the following generalized quadratic functional equation with n-independent variables in the spaces of generalized functions:
openaire +2 more sources
General Solution and Stability of Additive-Quadratic Functional Equation in IRN-Space
Journal of Function Spaces, 2021 The investigation of the stabilities of various types of equations is an interesting and evolving research area in the field of mathematical analysis. Recently, there are many research papers published on this topic, especially additive, quadratic, cubic,
K. Tamilvanan +4 more
doaj +1 more source
Linear Quadratic Stochastic Optimal Control Problems with Operator Coefficients: Open-Loop Solutions
, 2019 An optimal control problem is considered for linear stochastic differential equations with quadratic cost functional. The coefficients of the state equation and the weights in the cost functional are bounded operators on the spaces of square integrable ...
Wei, Qingmeng +2 more
core +1 more source
On the stability of set-valued functional equations with the fixed point alternative [PDF]
, 2012 Using the fixed point method, we prove the Hyers-Ulam stability of a Cauchy-Jensen type additive set-valued functional equation, a Jensen type additive-quadratic set-valued functional equation, a generalized quadratic set-valued functional equation and a
Choonkil Park +3 more
core +1 more source
Classification of generalized ternary quadratic quasigroup functional equations of the length three
Karpatsʹkì Matematičnì Publìkacìï, 2019 A functional equation is called: generalized if all functional variables are pairwise different; ternary if all its functional variables are ternary; quadratic if each individual variable has exactly two appearances; quasigroup if its solutions are ...
F.M. Sokhatsky, A.V. Tarasevych
doaj +1 more source
Mean-Field Stochastic Linear Quadratic Optimal Control Problems: Closed-Loop Solvability
, 2016 An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional. The coefficients and the weighting matrices in the cost functional are all assumed to be deterministic.
Li, Xun, Sun, Jingrui, Yong, Jiongmin
core +1 more source