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Abstract: We use the method of successive approximations and Faber polynomials to obtain an approximate solution of a dominant singular integral equation with Hölder continuous coefficients and conjugation on the Lyapunov curve. Moreover, the conditions of convergence in the L2 and H(ð›¼) spaces are presented. PubDate: 2022-04-28

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Abstract: The condition of strict differentiability strengthens the concept of differentiability, which is naturally applicable to the class of p-adic functions. We study the property of strict differentiability of finite-state isometries of the ring Z2. PubDate: 2022-04-28

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Abstract: We establish several general results concerning the partial sums of meromorphically starlike functions defined by means of a certain class of q-derivative (or q-difference) operators. The familiar concept of neighborhood for meromorphic functions is also considered. Moreover, by using a Ruscheweyh-type q-derivative operator, we define and study another new class of functions emerging from the class of normalized meromorphic functions. PubDate: 2022-04-28

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Abstract: We consider the problem of extreme partition of the complex plane well known in the geometric theory of functions. We obtain estimates for the maximum value of the product of some powers of inner radii of n disjoint domains in the complex plane with respect to n arbitrary points of the plane one of which can be located at infinity. The estimates established in the paper can be applied to various problems of the geometric theory of functions. PubDate: 2022-04-28

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Abstract: We study the behavior of a multidimensional singular integral operator in function spaces defined by the conditions imposed on the generalized oscillation of a function. PubDate: 2022-04-28

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Abstract: Two graphs are said to be Q-cospectral if they have the same signless Laplacian spectrum. A graph is said to be DQS if there are no other nonisomorphic graphs Q-cospectral with it. A tree is called double starlike if it has exactly two vertices of degree greater than 2. Let Hn(p, q) with n ≥ 2, p ≥ q ≥ 2, denote the double starlike tree obtained by attaching p pendant vertices to one pendant vertex of the path Pn and q pendant vertices to the other pendant vertex of Pn. We prove that Hn(p, q) is DQS for n ≥ 2, p ≥ q ≥ 2. PubDate: 2022-04-28

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Abstract: We prove that the ordinates of nontrivial zeros of the Lerch zeta-function are uniformly distributed modulo one. PubDate: 2022-04-28

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Abstract: We give an upper bound of the first-order Hankel determinant (H2(1)) for the classes of analytic functions. In addition, an estimate with Hankel determinant from below is given for the second angular derivative of an analytic function f(z) . For new inequalities, we used the results obtained for Jack’s lemma and Hankel’s determinant. Moreover, in a class of analytic functions on the unit disc, the estimates of the modulus of angular derivative from below are obtained under the assumption of existence of an angular limit on the boundary point. PubDate: 2022-04-28

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Abstract: We obtain differential convergence criteria for operator improper integrals and series. PubDate: 2022-04-28

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Abstract: We establish some new Hermite–Hadamard-type inequalities involving fractional integral operators with the exponential kernel. Meanwhile, we present many useful estimates for these types of new Hermite–Hadamard-type inequalities via exponentially convex functions. PubDate: 2022-04-28

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Abstract: We prove an identity with two parameters for a function differentiable with respect to another function via generalized integral operator. By applying the established identity, we discover the generalized trapezium, midpoint, and Simpson-type integral inequalities. It is indicated that the results of the present research provide integral inequalities for almost all fractional integrals discovered in recent decades. Various special cases are identified. Some applications of the presented results to special means and new error estimates for the trapezium and midpoint quadrature formulas are analyzed. The ideas and techniques of the present paper may stimulate further research in the field of integral inequalities. PubDate: 2022-04-28

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Abstract: We prove the existence of entire functions f of an arbitrary lower order ⋋ ≥ 0 and the order ðœŒ = ⋋ + 1 such that $$ \underset{r\to +\infty }{\lim \kern0.5em \operatorname{inf}T}\left(r+1,f\right)/T\left(r,f\right)>1. $$ The obtained results show that the condition ðœŒ − ⋋ < 1 in Valiron’s theorem cannot be improved. PubDate: 2022-02-03 DOI: 10.1007/s11253-022-01993-8

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Abstract: Let R be a ring and let SL(2,R) be the special linear group of 2 × 2 matrices with determinant 1 over R. We obtain the Wedderburn decomposition of \( \frac{{\mathbbm{F}}_q SL\left(2,{\mathbb{Z}}_3\right)}{J\left({\mathbbm{F}}_q SL\left(2,{\mathbb{Z}}_3\right)\right)} \) and show that \( 1+J\left({\mathbbm{F}}_q SL\left(2,{\mathbb{Z}}_3\right)\right) \) is a non-Abelian group, where ð”½q is a finite field with q = pk elements of characteristic 2 and 3. PubDate: 2022-02-03 DOI: 10.1007/s11253-022-01994-7

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Abstract: We present a survey of development of the concept of hidden symmetry in the field of partial differential equations, including a series of results previously obtained by the author. We also add new examples of the classes of equations with hidden symmetry of type II and explain the nature of the earlier established nonclassical symmetry of some equations. We suggest a constructive algorithm for the description of the classes of equations, which have specified conditional or hidden symmetry and/or can be reduced to equations with smaller number of independent variables by using a specific ansatz. We consider reductions existing due to the presence of Lie and conditional symmetry and also of the hidden symmetry of type II. We also discuss relationships between the concepts of hidden and conditional symmetry. It is shown that the hidden symmetry of type II earlier regarded as a separate type of non-Lie symmetry is caused, in fact, by the nontrivial Q-conditional symmetry of the reduced equations. The proposed approach enables us not only to find hidden symmetry and new reductions of the well-known equations but also to describe a general form of equations with given Q-conditional and type-II hidden symmetry. As an example, we describe the general classes of equations with hidden and conditional symmetry under rotations in the Lorentz and Euclid groups for which the corresponding hidden and conditional symmetry allows their reduction to radial equations with smaller number of independent variables. PubDate: 2022-02-03 DOI: 10.1007/s11253-022-01986-7

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Abstract: Let (pn) be a sequence of nonnegative numbers such that p0 > 0 and $$ {P}_n:= \sum \limits_{k=0}^n{p}_k\to \infty \kern1em \mathrm{as}\kern1em n\to \infty . $$ Let (un) be a sequence of fuzzy numbers. The weighted mean of (un) is defined by $$ {t}_n:= \frac{1}{P_n}\sum \limits_{k=0}^n{p}_k{u}_k\kern1em \mathrm{for}\kern1em n=0,1,2,\dots $$ It is known that the existence of the limit limun = μ0 implies that limtn = μ0. For the existence of the limit st-limtn = μ0, we require the boundedness of (un) in addition to the existence of the limit limun = μ0. However, in general, the converse of this implication is not true. We establish Tauberian conditions, under which the existence of the limit limun = μ0 follows from the existence of the limit limtn = μ0 or st-limtn = μ0. These Tauberian conditions are satisfied if (un) satisfies the two-sided condition of Hardy type relative to (Pn). PubDate: 2022-02-03 DOI: 10.1007/s11253-022-01989-4

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Abstract: We introduce the notion of Chebyshev derivations of the first and second kinds based on the polynomial algebra and the corresponding specific differential operators, find the elements of their kernels, and prove that any element of the kernel of each derivation specifies a polynomial identity for Chebyshev polynomials of both kinds. We deduce several polynomial identities for the Chebyshev polynomials of both kinds, for a partial case of Jacobi polynomials, and for the generalized hypergeometric function. PubDate: 2022-02-02 DOI: 10.1007/s11253-022-01985-8

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Abstract: We investigate the applications of slowly varying functions (in Karamata’s sense) to the theory of Markov branching processes. We treat the critical case so that the infinitesimal generating function of the process has the infinite second moment but regularly varies with the remainder. We improve the basic lemma of the theory of critical Markov branching processes and refine the known limit results. PubDate: 2022-02-02 DOI: 10.1007/s11253-022-01988-5

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Abstract: The aim of the present work is to weaken the conditions of monogeneity for functions taking values in a given three-dimensional commutative algebra over the field of complex numbers. The monogeneity of a function is understood as a combination of its continuity with the existence of Gâteaux derivative. PubDate: 2022-02-02 DOI: 10.1007/s11253-022-01991-w