Published in Mathematica Slovaca
We give some sufficient conditions for the convergence of the sequence of successive approximations to the unique solution of first order Cauchy problem in a Banach space. Our approach is based on a generalized Nagumo condition due to A. Constantin and the properties of the Kuratowski measure of noncompactness.
Published in Mathematica Slovaca
This paper studies analytic functions f defined on the open unit disk of the complex plane for which f/g and (1 + z)g/z are both functions with positive real part for some analytic function g. We determine radius constants of these functions to belong to classes of strong starlike functions, starlike functions of order α, parabolic starlike functio...
Published in Mathematica Slovaca
The aim of this study is to establish new discrete Grüss type inequality using fractional order h-sum and h-difference operators that generalize the fractional sum and difference operators.
Published in Mathematica Slovaca
Published in Mathematica Slovaca
The present paper introduces and studies the concepts of K-outer approximation and K-inner approximation for a monotone function μ defined on a D-poset P, by a subfamily K of P. Some desirable properties of K-approximable functions are established and it is shown that the family of all elements of P that possess K-approximation, forms a lattice and...
Published in Mathematica Slovaca
In this paper, a stochastic prey-predator model is investigated and analyzed, which possesses foraging arena scheme in polluted environments. Sufficient conditions are established for the extinction and persistence in the mean. These conditions provide a threshold that determines the persistence in the mean and extinction of species. Furthermore, i...
Published in Mathematica Slovaca
In this article we obtain sufficient conditions for the oscillation of all solutions of the higher-order delay difference equation Δm(yn−∑j=1kpnjyn−mj)+vnG(yσ(n))−unH(yα(n))=fn,$$\begin{array}{} \displaystyle \Delta^{m}\big(y_n-\sum_{j=1}^k p_n^j y_{n-m_j}\big) + v_nG(y_{\sigma(n)})-u_nH(y_{\alpha(n)})=f_n\,, \end{array}$$ where m is a positive int...
Published in Mathematica Slovaca
Published in Mathematica Slovaca
In this paper some properties of the pseudo-integral are summarized and a characterization theorem for this integral is proposed. Using the characterization theorem, we obtain that the pseudo-integral with respect to the pseudo-product of two σ-⊕-measures can be reduced to repeated pseudo-integrals. As a consequence of that claim and the Hölder typ...
Published in Mathematica Slovaca
Using the theory of elliptic curve, we show that all right triangles, such that the sum of the area and the square of the sum of legs is a square, are given by an infinite set. Similarly, we get all right triangles such that the sum of the area and the square of the semi-perimeter is a square. Using the theory of Pell’s equation, we prove that ther...
