On the stability of generalized gamma functional equation

We obtain the Hyers-Ulam stability and modified Hyers-Ulam stability for the equations of the form g(x+p)=φ(x)g(x) in the following settings: |g(x+p)−φ(x)g(x)|≤δ,   |g(x+p)−φ(x)g(x)|≤ϕ(x),   |(g(x+p)/φ(x)g(x))−1|≤ψ(x). As a consequence we obtain the stability theorems for the gamma functional equation

On Pexider Differences in Topological Vector Spaces

Let be a normed space and a sequentially complete Hausdorff topological vector space over the field ℚ of rational numbers. Let 1={(,)∈×∶‖‖+‖‖≥}, and 2={(,)∈×∶‖‖+‖‖0. We prove that the Pexiderized Jensen functional equation is stable for functions defined on 1(2), and taking values in . We consider also the Pexiderized Cauchy functional equation

On the Stability Problem in Fuzzy Banach Space

We investigate the generalized Ulam-Hyers stability of the Cauchy functional equation and pose two open problems in fuzzy Banach space

Nearly Quadratic Mappings over p

We establish some stability results over p-adic fields for the generalized quadratic functional equation ∑k=2n∑i1=2k∑i2=i1+1k+1⋯∑in-k+1=in-k+1nf(∑i=1,i≠i1,…,in-k+1nxi-∑r=1n-k+1xir)+f(∑i=1nxi)=2n-1∑i=1nf(xi), where n∈N and n≥2

Influence of Long-term Climate on Fatigue Life of Bridge Pier Concrete and a Reinforcement Method

This paper quantitatively evaluated the fatigue life of concrete around the air-water boundary layer of bridge piers located in inland rivers, considering the long-term climate. The paper suggests a method to predict the low-cycle fatigue life by demonstrating a thermal-fluid-structural analysis of bridge pier concrete according to long-term climate such as temperature, velocity and pressure of air and water in the process of freezing and thawing in winter. In addition, it proposes a reinforcing method to increase the life of damaged piers and proves the feasibility of the proposed method with numerical comparison experiment

Superstability of Some Pexider-Type Functional Equation

Abstract We will investigate the superstability of the sine functional equation from the following Pexider-type functional equation ( ), which can be considered the mixed functional equation of the sine and cosine functions, the mixed functional equation of the hyperbolic sine and hyperbolic cosine functions, and the exponential-type functional equations.</p

A STABILITY OF THE GENERALIZED SINE FUNCTIONAL EQUATIONS, II

ABSTRACT. The aim of this paper is to study the stability problem of the generalized sine functional equations as follows: ( ) 2 ( ) 2 x + y x + σy g(x)f(y) = f − f

SUPERSTABILITY OF THE DIFFERENCE-FORM FUNCTIONAL EQUATIONS RELATED TO DISTANCE MEASURES

Abstract. The present work extends the study on the stability of the functional equation f (pr,qs)+ f (ps,qr) = f (p,q) f (r,s) , which arises in the characterization of symmetrically compositive sum-form distance measures, and as a products of some multiplicative functions. In this paper, we obtain the superstability of the functional equations for all p,q,r,s ∈ G , where G is an Abelian group. These functional equations arise in the characterization of the nonsymmetrically compositive difference-form related to distance measures, products of some multiplicative functions. In reduction, they can be represented as exponential functional equations

On the Stability of Trigonometric Functional Equations

The aim of this paper is to study the superstability related to the d'Alembert, the Wilson, the sine functional equations for the trigonometric functional equations as follows: f(x+y)−f(x−y)=2f(x)g(y),f(x+y)−f(x−y)=2g(x)f(y)