Carlson type inequalities.
Category theorems concerning Z-density continuous functions
The ℑ-density topology on ℝ is a refinement of the natural topology. It is a category analogue of the density topology [9, 10]. This paper is concerned with ℑ-density continuous functions, i.e., the real functions that are continuous when the ℑ-densitytopology is used on the domain and the range. It is shown that the family of ordinary continuous functions f: [0,1]→ℝ which have at least one point of ℑ-density continuity is a first category subset of C([0,1])= f: [0,1]→ℝ: f is continuous equipped...
Cauchy means for signed measures.
Cauchy means of the Popoviciu type.
Cauchy Problem for Differential Equation with Caputo Derivative
The paper is devoted to the study of the Cauchy problem for a nonlinear differential equation of complex order with the Caputo fractional derivative. The equivalence of this problem and a nonlinear Volterra integral equation in the space of continuously differentiable functions is established. On the basis of this result, the existence and uniqueness of the solution of the considered Cauchy problem is proved. The approximate-iterative method by Dzjadyk is used to obtain the approximate solution...
Cauchy's means of Levinson type.
Cauchy's residue theorem for a class of real valued functions
Let be an interval in and let be a real valued function defined at the endpoints of and with a certain number of discontinuities within . Assuming to be differentiable on a set to the derivative , where is a subset of at whose points can take values or not be defined at all, we adopt the convention that and are equal to at all points of and show that , where denotes the total value of the Kurzweil-Henstock integral. The paper ends with a few examples that illustrate...
Cauchy-Schwarz and Hölder's inequalities are equivalent.
Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative
2000 Mathematics Subject Classification: 35A15, 44A15, 26A33The paper is devoted to the study of the Cauchy-type problem for the differential equation [...] involving the Riemann-Liouville partial fractional derivative of order α > 0 [...] and the Laplace operator.
Čebyšev's inequality on time scales.
Central Orderings in Fields of Real Meromorphic Function Germs.
Certain bounds for the differences of means.
Certain classes of analytic functions involving Sălăgean operator.
Certain higher monotonicity properties of Bessel functions
Certain higher monotonicity properties of -th derivatives of solutions of
Certain inequalities for convex functions.
Certain Properties of Fractional Calculus Operators Associated with Generalized Mittag-Leffler Function
Mathematics Subject Classification: 26A33, 33E12, 33C20.It has been shown that the fractional integration and differentiation operators transform such functions with power multipliers into the functions of the same form. Some of the results given earlier by Kilbas and Saigo follow as special cases.
Certain properties of generalized Orlicz spaces.
Cesàro-Perron-Stieltjes integral
Chain rules and p-variation
The main result is a Young-Stieltjes integral representation of the composition ϕ ∘ f of two functions f and ϕ such that for some α ∈ (0,1], ϕ has a derivative satisfying a Lipschitz condition of order α, and f has bounded p-variation for some p < 1 + α. If given α ∈ (0,1], the p-variation of f is bounded for some p < 2 + α, and ϕ has a second derivative satisfying a Lipschitz condition of order α, then a similar result holds with the Young-Stieltjes integral replaced by its extension.