The notions of compact convex variation and compact convex subdifferential for the mappings from a segment into a locally convex space (LCS) are studied. In the case of an arbitrary complete LCS, each indefinite Bochner integral has compact variation and each strongly absolutely continuous and compact subdifferentiable a.e. mapping is an indefinite Bochner integral. 0. Introduction and prelimin...

in this paper, quadratic rules for obtaining approximate solution of definite integrals as well as single and double integrals using spline quasi-interpolants will be illustrated. the method is applied to a few test examples to illustrate the accuracy and the implementation of the method

minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. also related inequalities to minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. several examples are given to illustrate the validity of theorems. some results on chebyshev and minkowski type inequalities are obtained.

in which a and b are continuously differentiate functions of two variables, fix) a continuously difierentiable function. The routine estimate of fadb gives bounds depending either on /| d/(x) | or on the maximum of | df/dx\ in the interval of integration. It is, however, possible, as shown in Theorem 1, to give a bound that is entirely independent'of the derivative of fix), and, consequently, t...

‎In this paper‎, ‎we find a relation between the proportionality factors which arise from the functional equations of two families of local Rankin-Selberg convolutions for‎ ‎irreducible admissible representations of orthogonal groups‎, ‎or unitary groups‎. ‎One family is that of local integrals of the doubling method‎, ‎and the other family is‎ ‎that of local integrals expressed in terms of sph...

Contents Preface v 1 Continuous-time stochastic processes 1 1.1 Measurability and stopping times. . Bibliography 133 iv CONTENTS Preface This monograph concerns itself with the theory of continuous-time martingales with continuous paths and the theory of stochastic integration with respect to continuous semimartingales. To set the scene for the theory to be developed, we consider an example. As...

*Correspondence: [email protected] College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China Abstract The main goal of the paper is to establish the boundedness of the fractional type Marcinkiewicz integralMβ ,ρ ,q on non-homogeneous metric measure space which includes the upper doubling and the geometrically doubling conditions. Under the a...

Much of the recent research on algorithmic randomness has focused on randomness for Lebesgue measure. While, from a computability theoretic point of view, the picture remains unchanged if one passes to arbitrary computable measures, interesting phenomena occur if one studies the the set of reals which are random for an arbitrary (continuous) probability measure or a generalized Hausdorff measur...

We discuss the feasibility of an elementary solution to the Diophantine equation of the 15 form x 2 + D = y n , where D > 1, n ≥ 3 and x > 0, called the Lebesgue–Nagell equation, which has recently been solved for 1 ≤ D ≤ 100 in [1].