Local–Global Minimum Property in Unconstrained Minimization Problems

The main goal of this paper is to prove some new results and extend some earlier ones about functions, which possess the so called local-global minimum property. In the last section, we show an application of these in the theory of calculus of variations

An Extension Theorem for Conditionally Additive Functions and Its Application for the Equality Problem of Quasi-Arithmetic Expressions

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Random means generated by random variables: expectation and limit theorems

We introduce the notion of a random mean generated by a random variable and give a construction of its expected value. We derive some sufficient conditions under which strong law of large numbers and some limit theorems hold for random means generated by the elements of a sequence of independent and identically distributed random variables.Comment: 25 page

Limit theorems for Bajraktarevi\'c and Cauchy quotient means of independent identically distributed random variables

We derive strong law of large numbers and central limit theorems for Bajraktarevi\'c, Gini and exponential- (also called Beta-type) and logarithmic Cauchy quotient means of independent identically distributed (i.i.d.) random variables. The exponential- and logarithmic Cauchy quotient means of a sequence of i.i.d. random variables behave asymptotically normal with the usual square root scaling just like the geometric means of the given random variables. Somewhat surprisingly, the multiplicative Cauchy quotient means of i.i.d. random variables behave asymptotically in a rather different way: in order to get a non-trivial normal limit distribution a time dependent centering is needed.Comment: 25 page

Homogeneity properties of subadditive functions

We collect, supplement and extend some well-known basic facts on various homogeneity properties of subadditive functions. Key Words: Homogeneous and subadditive functions, seminorms and pre- seminorms. AMS Classification Number: 39B7

Limit theorems for Bajraktarevic and Cauchy quotient means of independent identically distributed random variables

We derive strong laws of large numbers and central limit theorems for Bajraktarevic, Gini and exponential- (also called Beta-type) and logarithmic Cauchy quotient means of independent identically distributed (i.i.d.) random variables. The exponential- and logarithmic Cauchy quotient means of a sequence of i.i.d. random variables behave asymptotically normal with the usual square root scaling just like the geometric means of the given random variables. Somewhat surprisingly, the multiplicative Cauchy quotient means of i.i.d. random variables behave asymptotically in a rather different way: in order to get a non-trivial normal limit distribution a time dependent centering is needed

Bernstein-Doetsch type results for s-convex functions

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