On a characterization of -norm
On A Characterization Of Trigonometrical And Hyperbolic Functions By Functional Equations
On a Class of Fractional Type Integral Equations in Variable Exponent Spaces
2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30We obtain a criterion of Fredholmness and formula for the Fredholm index of a certain class of one-dimensional integral operators M with a weak singularity in the kernel, from the variable exponent Lebesgue space L^p(·) ([a, b], ?) to the Sobolev type space L^α,p(·) ([a, b], ?) of fractional smoothness. We also give formulas of closed form solutions ϕ ∈ L^p(·) of the 1st kind integral equation M0ϕ = f, known as the generalized...
On a class of sequences defined by using Riemann integral.
On a class of variational integrals over BV varieties
We present here our most recent results ([1def]) about the definition of non-linear Weiertrass-type integrals over BV varieties, possibly discontinuous and not necessarily Sobolev's.
On a Differential Equation with Left and Right Fractional Derivatives
Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05We treat the fractional order differential equation that contains the left and right Riemann-Liouville fractional derivatives. Such equations arise as the Euler-Lagrange equation in variational principles with fractional derivatives. We reduce the problem to a Fredholm integral equation and construct a solution in the space of continuous functions. Two competing approaches in formulating differential equations of fractional order...
On a Functional Equation in Connection with Derivations.
On a functional equation related to a generalization of Flett's mean value theorem.
On a Functional Equation Related to Iteration.
On a functional equation with asymptotically unique continuous solutions. (Short Communication).
On a functional equation with asymptotically unique continuous solutions.
On a functional inequality of Kemperman
On a generalisation of the Hahn-Jordan decomposition for real càdlàg functions
For a real càdlàg function f and a positive constant c we find another càdlàg function which has the smallest total variation among all functions uniformly approximating f with accuracy c/2. The solution is expressed in terms of truncated variation, upward truncated variation and downward truncated variation introduced in earlier work of the author. They are always finite even if the total variation of f is infinite, and they may be viewed as a generalisation of the Hahn-Jordan decomposition for...
On a generalization of Henstock-Kurzweil integrals
We study a scale of integrals on the real line motivated by the integral by Ball and Preiss and some recent multidimensional constructions of integral. These integrals are non-absolutely convergent and contain the Henstock-Kurzweil integral. Most of the results are of comparison nature. Further, we show that our indefinite integrals are a.e. approximately differentiable. An example of approximate discontinuity of an indefinite integral is also presented.
On a generalization of smooth and symmetric functions
On a generalization of the Hermite-Hadamard inequality. II.
On a generalization of the Lebesgue integral in
On a generalization of the Perron integral on one-dimensional intervals
On a generalization of -means.
On a generalized Dhombres functional equation. II.
We consider the functional equation where is a given increasing homeomorphism of an open interval and is an unknown continuous function. In a previous paper we proved that no continuous solution can cross the line where is a fixed point of , with a possible exception for . The range of any non-constant continuous solution is an interval whose end-points are fixed by and which contains in its interior no fixed point except for . We also gave a characterization of the class of continuous...