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Chaundy and Jolliffe [4] proved that if $\{a_{n}\}$ is a non-increasing (monotonic) real sequence with $\lim\limits_{n\to \infty}a_{n}=0$, then a necessary and sufficient condition for the uniform convergence of the series…

We consider a sequence of additive functionals {\phi_n}, set on a sequence of Markov chains {X_n} that weakly converges to a Markov process X. We give sufficient condition for such a sequence to converge in distribution, formulated in terms…

This note contains some observations on primary matrix functions and different notions of monotonicity with relevance towards constitutive relations in nonlinear elasticity. Focussing on primary matrix functions on the set of symmetric…

A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw's double inequality are proved to be completely monotonic. As applications of these results, the…

We prove generalized ABC theorems for vanishing sums of non-Archimedean entire functions of several variables in arbitrary characteristic.

We prove sharp Landau- and Schottky-type theorems for analytic functions which omit the $n$-th roots of unity. The proofs are based on a sharp lower bound for the Poincar\'e metric of the complex plane punctured at the roots of unity.

We give optimal effective bounds for some well-known theorems on complex algebraic surfaces, which are respectively due to Serre, Zariski (1962), Castelnuovo (1897), Artin (1962, 1966), Benveniste (1984), Cutkosky and Srinivas (1993). These…

In the paper, the authors concisely survey and review some functions involving the gamma function and its various ratios, simply state their logarithmically complete monotonicity and related results, and find necessary and sufficient…

Companions of Ostrowski's integral ineqaulity for absolutely continuous functions and applications for composite quadrature rules and for p.d.f.'s are provided.

We provide an example proving that there exists no quadratic Lyapunov function for a certain class of linear agreement/consensus algorithms, a fact that had been numerically verified in [5]. We also briefly discuss sufficient conditions for…

This work is in a stream initiated by a paper of Killip and Simon [Ann. of Math. (2003)]. Using methods of Functional Analysis and the classical Szeg\"o Theorem we prove sum rule identities in a very general form. Then, we apply the result…

Motivated by the Maximum Theorem for convex functions (in the setting of linear spaces) and for subadditive functions (in the setting of Abelian semigroups), we establish a Maximum Theorem for the class of generalized convex functions,…

We prove a matrix inequality for matrix monotone functions, and apply it to prove a singular value inequality for Heinz means recently conjectured by X. Zhan.

A theorem of Hoischen states that given a positive continuous function $\varepsilon:\mathbb{R}\to\mathbb{R}$, an integer $n\geq 0$, and a closed discrete set $E\subseteq\mathbb{R}$, any $C^n$ function $f:\mathbb{R}\to\mathbb{R}$ can be…

In this short note we show, providing counterexamples, that the "two important theorems" in the recent paper [Y, Yuan, Global optimization solutions to a class of non-convex quadratic minimization problems with quadratic constraints, in…

Expressions are not functions. Confusing the two concepts or failing to define the function that is computed by an expression weakens the rigour of interval arithmetic. We give such a definition and continue with the required re-statements…

A Central Limit Theorem for linear combinations of iterates of an inner function is proved. The main technical tool is Aleksandrov Desintegration Theorem for Aleksandrov-Clark measures.

We analyze and characterize maximal monotonicity of linear relations (set-valued operators with linear graphs). An important tool in our study are Fitzpatrick functions. The results obtained partially extend work on linear and at most…

In [K.J. Ciosmak, Applications of Strassen's theorem and Choquet theory to optimal transport problems, to uniformly convex functions and to uniformly smooth functions, Nonlinear Anal. 232 (2023), Paper No. 113267, 32 pp.], Theorem 2.3. does…

We study inequalities between general integral moduli of continuity of a function and the tail integral of its Fourier transform. We obtain, in particular, a refinement of a result due to D. B. H. Cline [2] (Theorem 1.1 below). We note that…