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Iteration is one of the most important topics in computer science and attentions are paid to functional equations involving iterates, one of which is the linear combination of alternative iterates. Recently existence, uniqueness and dependence for increasing Lipschitzian solutions were obtained for linear combination of alternative iterates on $ [0, 1] $ [ 0 , 1 ] and $ \mathbb {R} $ R in the case that all given functions are strictly increasing. In this paper we work in various cases of monotonicity (increasing and decreasing) among given functions and the unknown function. [ABSTRACT FROM AUTHOR]

In its additive version, Bohr–Mollerup's remarkable theorem states that the unique (up to an additive constant) convex solution f(x) to the equation Δ f (x) = ln x on the open half-line (0 , ∞) is the log-gamma function f (x) = ln Γ (x) , where Δ denotes the classical difference operator and Γ (x) denotes the Euler gamma function. In a recently published open access book, the authors provided and illustrated a far-reaching generalization of Bohr–Mollerup's theorem by considering the functional equation Δ f (x) = g (x) , where g can be chosen from a wide and rich class of functions that have convexity or concavity properties of any order. They also showed that the solutions f(x) arising from this generalization satisfy counterparts of many properties of the log-gamma function (or equivalently, the gamma function), including analogues of Bohr–Mollerup's theorem itself, Burnside's formula, Euler's infinite product, Euler's reflection formula, Gauss' limit, Gauss' multiplication formula, Gautschi's inequality, Legendre's duplication formula, Raabe's formula, Stirling's formula, Wallis's product formula, Weierstrass' infinite product, and Wendel's inequality for the gamma function. In this paper, we review the main results of this new and intriguing theory and provide an illustrative application. [ABSTRACT FROM AUTHOR]

We analyze in our paper questions of the theory of relativity. We approach this theory from the point of view of velocities and their composition. This is where the functional equations appear. Solving them leads to a world where velocities are bounded from above, the upper bound being exactly the "speed of light". [ABSTRACT FROM AUTHOR]

In fuzzy set theory, the migrativity among aggregation functions is a noteworthy topic from both theoretical and applied perspectives, numerous significant findings on the migrative functional equation for various combinations of particular subclasses of aggregation functions have been made in recent decades. Nonetheless, there are very few characterizations on migrativity of null-norms in the existing literature, and it has not been thoroughly studied. The present paper conducts an in-depth study on the migrativity of general grouping functions and general overlap functions with regard to null-norms. Firstly, by means of the ordinal sum representation of t-norms and t-conorms, we characterize the migrativity of general grouping functions with regard to t-norms and t-conorms, which shows some positive results. And then, we describe the structures of the solution of the migrative functional equation for general grouping functions with regard to null-norms. Finally, the migrativity of general overlap functions with regard to null-norms is discussed by duality. [ABSTRACT FROM AUTHOR]

We consider sequences of Steklov type operators and an associated functional equation. For a suitable sequence, we establish asymptotic formulas. [ABSTRACT FROM AUTHOR]

The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. Special attention is given to modelling such functions by systems of functional equations. [ABSTRACT FROM AUTHOR]

We present a complete constructive proof of the classical mountain-climbing theorem for two continuous piecewise monotone profiles. The proof strengthens the classical result, fills gaps omitted by previous proofs, provides information relevant to computational complexity, and illuminates how special properties of the separate profiles may be reflected in the functions that coordinate the movements of the two climbers. [ABSTRACT FROM AUTHOR]

In this work, we present the Cauchy functional equation in the context of connected Lie groups. We consider two generalizations of this equation with higher orders of the finite difference. [ABSTRACT FROM AUTHOR]

Motivated by the Szostok problem on functions with monotonic differences (2005, 2007), we consider a-Wright convex functions as a generalization of Wright convex functions. An application of these results to obtain new proofs of known results as well as new results is presented. [ABSTRACT FROM AUTHOR]