Related papers: Monotonicity patterns and functional inequalities …
New perspectives, proofs, and some extensions of known results are presented concerning the behavior of the Fitzpatrick function of a monotone type operator in the general context of a locally convex space.
The Lambert W function gives the solutions of a simple exponential polynomial. The generalized Lambert W function was defined by Mez\"{o} and Baricz, and has found applications in delay differential equations and physics. In this article we…
Some sharp two-sided Tur\'an type inequalities for parabolic cylinder functions and Tricomi confluent hypergeometric functions are deduced. The proofs are based on integral representations for quotients of parabolic cylinder functions and…
Matrix versions of some basic convexity inequalities are given. Further results on the same topic are proved in the recent papers on arxiv: 1. Hermitian operators and convex functions, 2. A concavity inequality for symmetric norms, 3.…
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…
We state some sufficient or equivalent conditions to GRH of general L-functions in terms of monotonicity of certain weighted summatory functions.
We characterize of the $q$-Bernstein functions in terms of $q$-Laplace transform. Moreover, we present several results of $q$-completely monotonic, $q$-log completely monotonic and $q$-Bernstein functions.
In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.
The main aim of this note, which can be viewed as a certain addendum to the paper \cite{2019}, is to propose several generalized inequalities for the ratio functions of trigonometric and hyperbolic functions. We basically follow the…
For displacement convex functionals in the probability space equip\-ped with the Monge-Kantorovich metric we prove the equivalence between the gradient and functional type \L oja\-sie\-wicz inequalities. \chg{We also discuss the more…
We obtain so far unproved properties of a ratio involving a class of Hermite and parabolic cylinder functions. Those ratios are shown to be strictly decreasing and bounded by universal constants. Differently to usual analytic approaches, we…
In this note we analyze the relationship between the properties of von Neumann-Morgenstern utility functions and expected utility functions. More precisely, we investigate which of the regularity and concavity assumptions usually imposed on…
In this paper, two new classes of convex functions as a generalization of convexity which is called (h-s)_{1,2}-convex functions are given. We also prove some Hadamard-type inequalities and applications to the special means are given.
In this note we prove some new results about the application of Wright functions of the first kind to solve fractional differential equations with variable coefficients. Then, we consider some applications of these results in order to…
The Wright function, which arises in the theory of the space-time fractional diffusion equation, is an interesting mathematical object which has diverse connections with other special and elementary functions. The Wright function provides a…
L$^\natural$ (natural)-convex functions encompass a large class of nonlinear functions over general integer domains and arise in a wide range of real-world applications. We explore the minimization of L$^\natural$-convex functions, of…
In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…
We give several unequivalent notions of convergency of meromorphic functions and more generally meromorphic mappings (strong, weak, $\Gamma $-convergency and some others). Relations between them are investigated. A version of Rouche theorem…
In the literature, the left-side of Hermite--Hadamard's inequality is called a midpoint type inequality. In this article, we obtain new integral inequalities of midpoint type for Riemann--Liouville fractional integrals of convex functions…
In this paper, we obtained some inequalities for \phi_{s}-convex function, \phi-Godunova-Levin function, \phi-P-function and log-\phi-convex function. Finally, we defined the class of \phi-quasi-convex functions and we examined some…