<abstract><p>Consider the problem of finding maximal nonpositive solvent $ \varPhi quadratic matrix equation (QME) X^2 + BX C = 0 with B being a nonsingular M $-matrix and an such that B^{-1}C\ge $. Such QME arises from overdamped vibrating system. Recently, under condition - I is $-matrix, Yu et al. (<italic>Appl. Math. Comput.</italic>, 218 (2011): 3303–3310) proved \r...

It is known that the satisfiability problem for equations over free partially commutative monoids is decidable but computationally hard. In this paper we consider the satisfiability problem for equations over free partially commutative monoids under the constraint that the solution is a subset of the alphabet. We prove that this problem is NP-complete for quadratic equations and that its unifor...

‎hensel [k‎. ‎hensel‎, ‎deutsch‎. ‎math‎. ‎verein‎, ‎{6} (1897), ‎83-88.] discovered the $p$-adic number as a‎ ‎number theoretical analogue of power series in complex analysis‎. ‎fix ‎a prime number $p$‎. ‎for any nonzero rational number $x$‎, ‎there‎ ‎exists a unique integer $n_x inmathbb{z}$ such that $x = ‎frac{a}{b}p^{n_x}$‎, ‎where $a$ and $b$ are integers not divisible by ‎$p$‎. ‎then $|x...

In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functional equation f(x+ y) + f(x− y) = 2f(x) + 2f(y) in non-Archimedean L-fuzzy normed spaces.

In this paper, we study the Hyers-Ulam-Rassias stability of the quadratic functional equation f(x + y) + f(x − y) = 2f(x) + 2f(y), x⊥y in which ⊥ is orthogonality in the sens of Rätz in modular spaces.

In this paper, the solution and the Hyers–Ulam stability of the following quadratic type functional equation k ∑ i=2 ∑ "j∈{−1,1} f (x1 + "jxi) = 2(k − 1)f(x1) + 2 k ∑

For a split reductive group $G$ over number field $k$, let $\rho$ be an $n$-dimensional complex representation of its dual $G^\vee(\mathbb{C})$. any irreducible cuspidal automorphic $\sigma$ $G(\mathbb{A})$, where $\mathbb{A}$ is the ring adeles in \cite{JL21}, authors introduce $(\sigma,\rho)$-Schwartz space $\mathcal{S}_{\sigma,\rho}(\mathbb{A}^\times)$ and $(\sigma,\rho)$-Fourier operator $\...

In this paper, we give a general solution of a refined quadratic functional equation and then investigate its generalized Hyers–Ulam stability in quasi-normed spaces and in non-Archimedean normed spaces. AMS Subject Classification: 39B82, 39B62

In this paper, we obtain the general solution and investigate the generalized Hyers-Ulam stability of the new generalized mixed type additive and quadratic functional equation in fuzzy normed space. Mathematics Subject Classification 39B55, 39B52, 39B82

and Applied Analysis 3 for x, y, z ∈ A. A Banach non-Archimedean ternary algebra is a normed non-Archimedean ternary algebra such that the normed non-Archimedean vector space with norm ‖ · ‖ is complete. The ternary algebras have been studied in nineteenth century. Their structures appeared more or less naturally in various domains of mathematical physics and data processing. The discovery of t...