A Monte Carlo Method for High Dimensional Integration.
A more generalized Gronwall-like integral inequality with applications.
A multidimensional analogue of the Denjoy-Perron-Henstock-Kurzweil integral.
A multidimensional integration by parts formula for the Henstock-Kurzweil integral
It is shown that if is of bounded variation in the sense of Hardy-Krause on , then is of bounded variation there. As a result, we obtain a simple proof of Kurzweil’s multidimensional integration by parts formula.
A multidimensional Taylor's theorem with minimal hypothesis
A multiple Hardy-Hilbert integral inequality with the best constant factor.
A multiple Hilbert-type integral inequality with the best constant factor.
A multiplicative embedding inequality in Orlicz--Sobolev spaces.
A necessary and sufficient condition for continuity of additive functions
A new algorithm for approximating the least concave majorant
The least concave majorant, , of a continuous function on a closed interval, , is defined by We present an algorithm, in the spirit of the Jarvis March, to approximate the least concave majorant of a differentiable piecewise polynomial function of degree at most three on . Given any function , it can be well-approximated on by a clamped cubic spline . We show that is then a good approximation to . We give two examples, one to illustrate, the other to apply our algorithm.
A new and more powerful concept of the PU-integral
A new application of the homotopy analysis method in solving the fractional Volterra's population system
This paper considers a Volterra's population system of fractional order and describes a bi-parametric homotopy analysis method for solving this system. The homotopy method offers a possibility to increase the convergence region of the series solution. Two examples are presented to illustrate the convergence and accuracy of the method to the solution. Further, we define the averaged residual error to show that the obtained results have reasonable accuracy.
A New Approach to Fuzzy Arithmetic
This work shows an application of a generalized approach for constructing dilation-erosion adjunctions on fuzzy sets. More precisely, operations on fuzzy quantities and fuzzy numbers are considered. By the generalized approach an analogy with the well known interval computations could be drawn and thus we can define outer and inner operations on fuzzy objects. These operations are found to be useful in the control of bioprocesses, ecology and other domains where data uncertainties exist.* This work...
A new approach to Ky Fan-type inequalities.
A New Characterization of Weighted Peetre K-Functionals (II)
2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10. ∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”, Sofia, 2006.Certain types of weighted Peetre K-functionals are characterized by means of the classical moduli of smoothness taken on a proper linear transforms of the function. The weights with power-type asymptotic at the ends of the interval with arbitrary real exponents are considered. This paper extends the method and results presented...
A new class of analytic functions involving certain fractional derivative operators.
A new delay vector integral inequality and its application.
A new extension of Hilbert's inequality for multifunctions with best constant factors.
A new extension of monotone sequences and its applications.
A new generalization of Ostrowski type inequality on time scales.