The aim of this paper is to give some refinements to several inequalities, recently etablished, by P.K. Bhandari and S.K. Bissu in [Inequalities via Hölder’s inequality, Scholars Journal of Research in Mathematics and Computer Science, 2 (2018), no. 2, 124–129] for the incomplete gamma function, Polygamma functions, Exponential integral function, Abramowitz function, Hurwitz-Lerch zeta function and for the normalizing constant of the generalized inverse Gaussian distribution and the Remainder of the Binet’s first formula for ln Γ(x).

We present a local convergence analysis of the super-Halley-like method in order to approximate a locally unique solution of an equation in a Banach space setting. The convergence analysis in earlier studies was based on hypotheses reaching up to the third derivative of the operator. In the present study we expand the applicability of the super-Halley-like method by using hypotheses up to the second derivative. We also provide: a computable error on the distances involved and a uniqueness result based on Lipschitz constants. Numerical examples are also presented in this study.

We give a proposal of generalization of the Freese–Nation property for topological spaces. We introduce a few properties related to Freese–Nation property: FNS, FN, FNS^*, FNI. This article presents some relationship between these concepts. We show that spaces with the FNS property satisfy ccc and any product of such spaces also satisfies ccc. We show that all metrizable spaces have the FN property.

In this paper, we obtain a closed form for F_{Σ_{i=1}^k}, P_{Σ_{i=1}^k} and J_{Σ_{i=1}^k} for some positive integers k where F_r, P_r and J_r are the rth Fibonacci, Pell and Jacobsthal numbers, respectively. We also give three open problems for the general cases F_{Σ_{i=1}^n}, P_{Σ_{i=1}^n} and J_{Σ_{i=1}^n} for any arbitrary positive integer n.

In this paper we present a new one parameter generalization of the classical Pell numbers. We investigate the generalized Binet’s formula, the generating function and some identities for r-Pell numbers. Moreover, we give a graph interpretation of these numbers.

Investigating Hyers–Ulam stability of the additive Cauchy equation with domain in a group G, in order to obtain an additive function approximating the given almost additive one we need some properties of G, starting from commutativity to others more sophisticated. The aim of this survey is to present these properties and compare, as far as possible, the classes of groups
involved.

Let Alg N be a nest algebra associated with the nest N on a (real or complex) Banach space X. Suppose that there exists a non-trivial idempotent P∈Alg N with range P(X)∈?N, and δ:Alg N→Alg N is a continuous linear mapping (generalized) left derivable at P, i.e. δ(ab) = aδ(b) + bδ(a) (δ(ab) = aδ(b) + bδ(a) - baδ(I)) for any a,b∈Alg N with ab = P, where I is the identity element of AlgN. We show that δ is a (generalized) Jordan left derivation. Moreover, in a strongly operator topology we characterize continuous linear maps on some nest algebras Alg???? with the property that δ(P) = 2Pδ(P) or δ(P) = 2Pδ(P) - Pδ(I) for every idempotent P in Alg N.

In this work we generalize the results of [9] to the higher level case: we define n-th root selections in fields of characteristic ≠2, that is subgroups of the multiplicative group of a field whose existence is equivalent to the existence of a partial inverse of the x↦xⁿ function, provide necessary and sufficient conditions for such a subgroup to exist, study their existence under field extensions, and give some structural results describing the behaviour of maximal n-th root selection fields.

Non-markovian queueing systems can be extended to piecewisedeterministic Markov processes by appending supplementary variables to the system. Then their analysis leads to an infinite system of partial differential equations with an infinite number of variables and non-local boundary conditions. We show how one can study such systems by using the theory of stochastic semigroups.

In this paper we study the nature of Ricci solitons in D-homothetically deformed Kenmotsu manifolds. We prove that η-Einstein Kenmotsu metric as a Ricci soliton remains η-Einstein under D-homothetic deformation and the scalar curvature remains constant.

The usual way of solving a solvable quintic equation has been to establish more equations than unknowns, so that some relation among the coefficients comes up, leading to the solutions. In this paper, a relation among the coefficients of a principal quintic equation is established by effecting a change of variable and inserting a root to the quintic equation, and then equating oddpowers of the resulting sextic equation to zero. This leads to an even-powered sextic equation, or equivalently a cubic equation; thus one needs to solve the cubic equation.
We break from this tradition, rather factor the even-powered sextic equation in a novel fashion, such that the inserted root is identified quickly along with one root of the quintic equation in a quadratic factor of the form, u² - g² = (u + g)(u - g). Thus there is no need to solve any cubic equation. As an extra benefit, this root is a function of only one coefficient of the given quintic equation.

In this paper the authors aspire to obtain the approximate analytical solution of Modified Burgers Equation with newly defined conformable derivative by employing homotopy analysis method (HAM).

This work is devoted to the generalization of previous results on Gleason measures to complex Gleason measures. We develop a functional calculus for complex measures in relation to the Nemytsky operator. Furthermore we present and discuss the interpretation of our results with applications in the field of quantum mechanics. Some concrete examples and further extensions of several theorems are also presented.

Let F be an endofunctor of a category C. We prove isomorphism theorems for F-coalgebras under condition that the underlying category C is exact; that is, regular with exact sequences. Also, F is not assumed to preserve pullbacks.

In this article, we establish some non-unique fixed point theorems of Ćirić’s type for (Φ,ψ)-hybrid contractive mappings by using a similar notion to that of the paper [M. Akram, A.A. Zafar and A.A. Siddiqui, A general class of contractions: A-contractions, Novi Sad J. Math. 38 (2008), no. 1, 25–33]. Our results generalize, extend and improve several ones in the literature.

In this paper we consider the finite groups that act fiber- and orientation-preservingly on closed, compact, and orientable Seifert manifolds that fiber over an orientable base space. We establish a method of constructing such group actions and then show that if an action satisfies a condition on the obstruction class of the Seifert manifold, it can be derived from the given construction. The obstruction condition is refined and the general structure of the finite groups that act via the construction is provided.

Let R be a prime ring with center Z(R). A map G:R→R is called a multiplicative (generalized) (α,β)-derivation if G(xy) = G(x)α(y)+β(x)g(y) is fulfilled for all x,y∈R, where g:R→R is any map (not necessarily derivation) and α,β:R→R are automorphisms. Suppose that G and H are two multiplicative (generalized) (α,β)-derivations associated with the mappings g and h, respectively, on R and α,β are automorphisms of R. The main objective of the present paper is to investigate the following algebraic identities: (i) G(xy) + α(xy) = 0, (ii) G(xy) + α(yx) = 0, (iii) G(xy) + G(x)G(y) = 0, (iv) G(xy) = α(y) ◦ H(x) and (v) G(xy) = [α(y),H(x)] for all x,y in an appropriate subset of R.

The hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper we consider special kinds of hybrid numbers, namely the Jacobsthal and the Jacobsthal-Lucas hybrid numbers and we give some their properties.

If G is a finite group, then a bijective function f:G→G is inverse ambiguous if and only if f(x)^{-1 =} f^-1(x) for all x∈G. We give a precise description when a finite group admits an inverse ambiguous function and when a finite group admits an inverse ambiguous automorphism.

In this paper we will introduce the concept of weighted reproducing kernel of l²(ℂ) space, in similiar way as it is done in case of weighted reproducing kernel of Bergman space. We will give an explicit formula for it and prove that it depends analytically on weight. In addition, we will show some theorems about dependance of l²(ℂ) space on weight.

Report of Meeting. The Nineteenth Katowice–Debrecen Winter Seminar on Functional Equations and Inequalities Zakopane (Poland), January 30–February 2, 2019.