A functional equation involving f and $f^{-1}$.

CONNECTED AND DISCONNECTED PLANE SETS AND THE FUNCTIONAL EQUATION f(x)+f(y)=f(x+y)

Cauchy discovered before 1821 that a function satisfying the equation ƒ(*)+ƒ (y) =f(* + y) is either continuous or totally discontinuous. After Hamel showed the existence of a discontinuous function satisfying the equation, many mathematicians have concerned themselves with problems arising from the study of such functions. However the following question seems to have gone unanswered : Since th...

A Fixed Point Approach to the Stability of the Functional Equation f(x+y)=F[f(x),f(y)]

In 1940, Ulam 1 gave a wide ranging talk before the mathematics club of the University of Wisconsin in which he discussed a number of important unsolved problems. Among those was the question concerning the stability of group homomorphisms: “Let G1 be a group and let G2 be a metric group with the metric d ·, · . Given ε > 0, does there exist a δ > 0 such that if a function h : G1 → G2 satisfies...

نامساوی های زیرجمعی ماتریسی برای (f(a+b و(f(a)+f(b

در سال 1999 اندو وژان یک نامساوی زیر جمعی برای توابع مقعر عملگری بدست آوردند. ما این نامساوی را به همه توابع مقعر توسعه می دهیم: ماتریس های نیمه معین مثبت a وb تابع مقعر غیرمنفی f روی (&,0] را در نظر می گیریم. برایس هر نرم متقرن داریم. ||| (f(a)+f(b) ||| > |||f(a+b)|||

Functional Equation f x pf x − 1 − qf x − 2 and Its Hyers - Ulam Stability

F eb 2 01 1 A Master Equation Approach to the ‘ 3 + 1 ’ Dirac Equation

A derivation of the Dirac equation in ‘3 + 1’ dimensions is presented based on a master equation approach originally developed for the ‘1+ 1’ problem by McKeon and Ord. The method of derivation presented here suggests a mechanism by which the work of Knuth and Bahrenyi on causal sets may be extended to a derivation of the Dirac equation in the context of an inference problem.