The aim of this paper is to obtain some new bounds having Riemann type quantum integrals within the class of strongly convex functions. The results obtained are sharp on limit q → 1. These new results reduce to Tariboon-Ntouyas, Merentes-Nikodem and other previously known results when q → 1, where 0 < q < 1. The sharpness of the results of Tariboon-Ntouyas and Merentes-Nikodem is proved as a consequence.
We prove that the local time process of a planar simple random walk, when time is scaled logarithmically, converges to a non-degenerate pure jump process. The convergence takes place in the Skorokhod space with respect to the M1 topology and fails to hold in the J1 topology.
Consider a two-dimensional discrete random variable (X, Y) with possible values 1, 2, . . . , I for X and 1, 2, . . . , J for Y. For specifying the distribution of (X, Y), suppose both conditional distributions of X given Y and Y given X are specified. In this paper, we address the problem of determining whether a given set of constraints involving marginal and conditional probabilities and expectations of functions are compatible or most nearly compatible. To this end, we incorporate all those information with the Kullback-Leibler (K-L) divergence and power divergence statistics to obtain the most nearly compatible probability distribution when the two conditionals are not compatible, under the discrete set up. Finally, a comparative study is carried out between the K-L divergence and power divergence statistics for some illustrative examples.
The Rayleigh distribution is an important model in applications such as noise theory, height of the sea waves and wave length. In this paper, we first study the reliability characteristics of Morgenstern type bivariate Rayleigh distribution (MTBRD). Then, we investigate some properties on concomitants of order statistics and record values in MTBRD. Finally, we propose the best linear unbiased estimator for a parameter of MTBRD using both complete and censored samples based on concomitants of order statistics.
In this paper, we get integral representations for the quintic Airy functions as the four linearly independent solutions of differential equation y(4) + xy = 0. Also, new integral representations for the products of these functions are obtained in terms of the Bessel functions and the Riesz fractional derivatives of these products are given.
The appropriate estimation of incurred but not reported (IBNR) reserves is traditionally one of the most important task for property and casualty actuaries. As certain claims are reported considerably later after their occurrence, the amount and appropriateness of the reserves have a substantial effect on the financial results of institutions. In recent years, stochastic reserving methods have become increasingly widespread, supported by broad actuarial literature, describing development models and evaluation techniques.
The cardinal aim of the present paper is to compare the appropriateness of several stochastic estimation methods, supposing different distributional underlying development models. For lack of analytical formulae in most of the model settings relevant from a practical perspective, due to the complex behavior of summed variables, simulations are performed to approximate distributions and results. Considering that the number of runoff triangles is generally limited, stochastically simulated scenarios contribute to feasible solutions. Stochastic reserving is taken into account as a stochastic forecast, thus comparison techniques developed for stochastic forecasts can be applied, opening up new informative perspectives beyond classical prediction measures, such as the mean square error of prediction.
Based on an original idea, i.e., a special way of choosing the indexes of the involved mappings, we propose a new iterative algorithm for approximating common fixed points of a sequence of nonexpansive nonself mappings, and some convergence theorems are established in the framework of CAT(0) spaces. Our results extend the previous results restricted to the situation of a single mapping.
A space X is of countable type (resp. subcountable type) if every compact subspace F of X is contained in a compact subspace K that is of countable character (resp. countable pseudocharacter) in X. In this paper, we mainly show that: (1) For a functionally Hausdorff space X, the free paratopological group FP(X)and the free abelian paratopological group AP(X) are of countable type if and only if X is discrete; (2) For a functionally Hausdorff space X, if the free abelian paratopological group AP(X) is of subcountable type then X has countable pseudocharacter. Moreover, we also show that, for an arbitrary Hausdorff μ-space X, if AP2(X) or FP2(X) is locally compact, then X is a topological sum of a compact space and a discrete space.
In this paper, we study the existence of multiple solutions for a class of impulsive perturbed elastic beam equations of Kirchhoff-type. We give a new criteria for guaranteeing that the impulsive perturbed elastic beam equations of Kirchhoff-type have at least three generalized solutions by using a variational method and a critical points theorem of B. Ricceri.
By making use of the critical point theory, we establish some new existence criteria to guarantee that a 2nth-order nonlinear difference equation containing both advance and retardation with p-Laplacian has a nontrivial homoclinic orbit. Our conditions on the potential are rather relaxed, and some existing results in the literature are improved.