In this paper, the authors established the generalized Ulam Hyers stability of additive functional equation    

in this paper, using the fixed point and direct methods, we prove the generalized hyers-ulam-rassias stability of the following cauchy-jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. the concept of hyers-ulam-rassias stability originated from th. m. rassias’ stability theorem t...

using fixed point method, we prove some new stability results for lie $(alpha,beta,gamma)$-derivations and lie $c^{ast}$-algebra homomorphisms on lie $c^{ast}$-algebras associated with the euler-lagrange type additive functional equation begin{align*} sum^{n}_{j=1}f{bigg(-r_{j}x_{j}+sum_{1leq i leq n, ineq j}r_{i}x_{i}bigg)}+2sum^{n}_{i=1}r_{i}f(x_{i})=nf{bigg(sum^{n}_{i=1}r_{i}x_{i}bigg)} end{...

All strictly monotonic solutions of a general functional equation are determined. In a particular case, which plays an essential role in the axiomatization of rank-dependent expected utility, all nonnegative solutions are obtained without any regularity conditions. An unexpected possibility of reduction to convexity makes the present proof possible.

1. Proofs of Theorems 1 and 2. Let η = (η T 1 , · · · , η T p) T be a (pq n)-vector and Θ = (Θ 1 , · · · , Θ p) be an n × (pq n) matrix. With matrix notation, the linear FAR criterion minimizes the following objective function

Stochastic nonlinear elliptic partial differential equations with white noise disturbances are studied in the countably additive measure set up. Introducing the Onsager-Machlup function to the system model, the smoothing problem for maximizing the modified likelihood functional is solved and the explicit form of nonlinear smoother is presented in the finitely additive observation noise set up. ...

A major challenge in tissue engineering is the generation of cell-seeded implants with structures that mimic native tissue, both in anatomic geometries and intratissue cell distributions. By combining the strengths of injection molding tissue engineering with those of Solid Freeform Fabrication (SFF), three-dimensional preseeded implants were fabricated without custom-tooling, enabling efficien...

This paper deals with a functional equation connected with the Shannon entropy, the entropy of degree fi and others. There are so many algebraic properties which are satisfied by them. Various systems of axioms were used, in literature, to characterize them. Let A„ = {P = (p1, ..., pn)jpi ^ 0, Y,Pt = 1} t> e t n e s e t °f a ' l finite complete discrete probability distributions on a given part...

7"o(z) being employed in general to denote the total variation of the function z(t) on /. Thus metrised, (BV) is not a Banach space(2); but it is complete, separable, and boundedly compact. Although a linear space, it is not a "linear topological space" in the sense in which that term is sometimes used, for the topology introduced by the metric (1) is non-uniform. Indeed it is easily seen that ...