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This work deals with basic approximation problems such as direct, inverse and simultaneous theorems of trigonometric approximation of functions of weighted Lebesgue spaces with a variable exponent on weights satisfying a variable Muckenhoupt A p (··) type condition. Several applications of these...
In 2005, Tkebuchava constructed a set of logarithmic summation methods which includes Riesz and Nöörlund logarithmic summation methods as limit cases. He gave estimates for the kernels of a trigonometric system and also some consequences with respect to the convergence of the means of a Fourier...
For a given topological space E , some properties of absolutely nonmeasurable real-valued functions, with respect to a certain class of measures on E , are considered. These functions are compared with Sierpińński––Zygmund type real-valued functions on E which have the property that they are...
We obtain the necessary and sufficient conditions for the boundedness of the weighted singular integral operator with power weights in grand Lebesgue spaces. Because of applications to singular integral equations, the underlying set on which the functions are defined is a Carleson curve in the...
A generalization of the Euler beta function to the case of a multi-dimensional variable is defined. In this context, the original beta function is a function of a two-dimensional variable. An analogue of the Euler formula for this new function is derived for the case of a three-dimensional...
Let ℱℱ be a family of meromorphic functions in a domain D ; let k ≥≥ 2 be a positive integer; and let a, b and c be complex numbers such that b ≠≠ 0 and a ≠≠ c . If, for each ƒƒ ∈∈ ℱℱ, all zeros of ƒƒ have multiplicity at least k , ƒƒ( z ) == a ⇔⇔ D (ƒƒ) == b , and D (ƒƒ) == 0 ⇒⇒ ƒƒ( z ) == c ,...
The purpose of this paper is to present some fixed point results for self-generalized (singlevalued and multivalued) contractions in ordered metric spaces and in metric spaces endowed with a graph. Our theorems generalize and extend some recent results in the literature.
We consider the cutting process of the generalized Mööbius––Listing surface along some closed line which is parallel to its border line. We show connections of the resulting mathematical objects with the set of knots and links. In some cases we count the indices of the corresponding objects...
Variation formulas of solution are proved for a non-linear differential equation with constant delay. In this paper, the essential novelty is the effect of delay perturbation in the variation formulas. The continuity of the initial condition means that the values of the initial function and the...
An admissibility for topological degree of variable Lebesgue, Besov and Triebel––Lizorkin spaces is given.
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