Generalized Hyers-Ulam Stability for a General Mixed Functional Equation in Quasi-��-normed Spaces

In this paper, we establish the general solution and investigate the generalized Hyers-Ulam stability of the following mixed additive and quadratic functional equation

A half-discrete Hilbert-type inequality in the whole plane related to the Riemann zeta function

By the use of Hermite–Hadamard’s inequality and weight functions, a half-discrete Hilbert-type inequality in the whole plane with the kernel of hyperbolic cotangent function and multi-parameters is given. The constant factor related to the Riemann zeta function is proved to be the best possible. The equivalent forms, two kinds of particular inequalities, the operator expressions and some equivalent reverses are considered.     

A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES＊

Using a fixed-point method,we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation:f(kx + y) + f(kx - y) =kf(x + y) + kf(x -y) + 2f(kx) - 2kf(x) in Banach modules o...     

The N-Isometric Isomorphisms in Linear N-Normed C^＊-Algebras

We prove the Hyers-Ulam stability of linear N-isometries in linear N-normed Banach mod- ules over a unital C^＊-algebra. The main purpose of this paper is to investigate N-isometric C^＊-algebra isomorphisms between linear N-normed C^＊-algebras, N-isometric Poisson C^＊-algebra isomorphisms between linear N-normed Poisson C^＊-algebras, N-isometric Lie C^＊-algebra isomorphisms between linear N-normed Lie C^＊-algebras, N-isometric Poisson JC^＊-algebra isomorphisms between linear N-normed Poisson JC^＊-algebras, and N-isometric Lie JC^＊-algebra isomorphisms between linear N-normed Lie JC^＊-algebras. Moreover, we prove the Hyers- Ulam stability of t：heir N-isometric homomorphisms.     

A maximum principle in Rn + 1

In this paper we establish maximum principles of the Cauchy problem for hyperbolic equations in $\text{R}$³ and $\text{R}$^{n + 1}(n ? 2). Our maximum principles generalize the results of Weinberger [5], and Sather [3, 4] for a class of equations such that the coefficients can be allowed to depend upon t, as well, in {x₁, x₂, t}-space and {x₁, x₂,…, x_n, t}-space. Throughout this paper, the influence of the work of Douglis [1] is apparent. See [2].     

Optimal parameter selections for a general Halpern iteration

Numerical Algorithms - Let C be a closed affine subset of a real Hilbert space H and $T:C rightarrow C$ be a nonexpansive mapping. In this paper, for any fixed u ∈ C, a general Halpern...     

Hyers-Ulam stability of a general linear partial differential equation

Aequationes mathematicae - In this paper we will study Hyers-Ulam stability for a general linear partial differential equation of first order in a Banach space.     

The rate of growth of moments of certain cotangent sums

We consider cotangent sums associated to the zeros of the Estermann zeta function considered by the authors in their previous paper (Maier and Rassias, Generalizations of a cotangent sum associated to the Estermann zeta function, 2014). We settle a question on the rate of growth of the moments of these cotangent sums left open in Maier and Rassias (Generalizations of a cotangent sum associated to the Estermann zeta function, 2014), and obtain a simpler proof of the equidistribution of these sums.     

Noise in the operating rooms of Greek hospitals

This study is an evaluation of the problem of noise pollution in operating rooms. The high sound pressure level of noise in the operating theatre has a negative impact on communication between operating room personnel. The research took place at nine Greek public hospitals with more than 400 beds. The objective evaluation consisted of sound pressure level measurements in terms of L(eq), as well as peak sound pressure levels in recordings during 43 surgeries in order to identify sources of noise. The subjective evaluation consisted of a questionnaire answered by 684 operating room personnel. The views of operating room personnel were studied using Pearson's X(2) Test and Fisher's Exact Test (SPSS Version 10.00), a t-test comparison was made of mean sound pressure levels, and the relationship of measurement duration and sound pressure level was examined using linear regression analysis (SPSS Version 13.00). The sound pressure levels of noise per operation and the sources of noise varied. The maximum measured level of noise during the main procedure of an operation was measured at L(eq)=71.9 dB(A), L(1)=84.7 dB(A), L(10)=76.2 dB(A), and L(99)=56.7 dB(A). The hospital building, machinery, tools, and people in the operating room were the main noise factors. In order to eliminate excess noise in the operating room it may be necessary to adopt a multidisciplinary approach. An improvement in environment (background noise levels), the implementation of effective standards, and the focusing of the surgical team on noise matters are considered necessary changes.