Showing papers in "Kyungpook Mathematical Journal in 2021"

Univalent Functions Associated with the Symmetric Points and Cardioid-shaped Domain Involving (p,q)-calculus

Abstract: In this paper, we introduce new classes of post-quantum or (p, q)-starlike and convex functions with respect to symmetric points associated with a cardiod-shaped domain. We obtain (p, q)-Fekete-Szegö inequalities for functions in these classes. We also obtain estimates of initial (p, q)-logarithmic coefficients. In addition, we get q-Bieberbachde-Branges type inequalities for the special case of our classes when p = 1. Moreover, we also discuss some special cases of the obtained results.

Two Extensions of a Star Operation on D to the Polynomial Ring D[X]

Abstract: Let D be an integral domain with quotient field K, X an indeterminate over D, ∗ a star operation on D, and Cl∗(D) be the ∗-class group of D. The ∗w-operation on D is a star operation defined by I∗w = {x ∈ K | xJ ⊆ I for a nonzero finitely generated ideal J of D with J∗ = D}. In this paper, we study two star operations {∗} and [∗] on D[X] defined by A{∗} = ⋂ P∈∗w-Max(D) ADP [X] and A [∗] = ( ⋂ P∈∗w-Max(D) AD[X]P [X]) ∩ AK[X]. Among other things, we show that Cl∗(D) ∼= Cl[∗](D[X]) if and only if D is integrally

MHD Pulsatile Flow and Heat Transfer of Two Immiscible Couple Stress Fluids Between Permeable Beds

Abstract: Abstract. The present paper addresses magnetohydrodynamic pulsating flow and heat transfer of two immiscible, incompressible, and conducting couple stress fluids between two permeable beds. The flow between the permeable beds is assumed to be governed by Stokes’ [28] couple stress fluid flow equations, whereas the dynamics of permeable beds is determined by Darcy’s law. In this study, matching conditions were used at the fluid– fluid interface, whereas the B-J slip boundary condition was employed at the fluid–porous interface. The governing equations were solved analytically, and the expressions for velocity, temperature, mass flux, skin friction, and rate of heat transfer were obtained. The analytical expressions were numerically evaluated, and the results are presented through graphs and tables.

Existence of Positive Solutions for a Class of Conformable Fractional Differential Equations with Parameterized Integral Boundary Conditions

Abstract: Fractional calculus and fractional differential equations are recently experiencing rapid development. There are several notions of fractional derivatives, some classical, such as the Riemann-Liouville or Caputo definitions, and some novel, such as conformable fractional derivatives [18], β-derivatives [9], or others [12, 20]. Recently, the new definition of a conformable fractional derivative, given by [1, 2, 18], has drawn much interest from many researchers [6, 7, 17, 22, 23, 24, 26]. Recent results on conformable fractional differential equations can also be found in [3, 8, 11]. In 2017, X. Dong et al.[15] studied the existence and multiplicity of positive solutions for the following conformable fractional differential equation with p-Laplacian operator D(φp(D u(t))) = f(t, u(t)), 0 < t < 1, u(0) = u(1) = Du(0) = Du(1) = 0. Here, 1 < α ≤ 2 is a real number, D is the conformable fractional derivative, φp(s) = |s|p−2s, p > 1, φ−1 p = φq, 1/p+ 1/q = 1, and f : [0, 1]× [0,+∞)→ [0,+∞)

On the Spectrum Discreteness for the Magnetic Schrödinger Operator on Quantum Graphs

Abstract: For the operator describing a physical system, it is an ongoing problem to describe which properties the system characterise when the spectrum of the operator is discrete. This problem has been solved in various special cases. For example, Molchanov proposed in [12] a criterion for a potential to provide the discreteness of the Hamiltonian spectrum in the 1-dimensional case. Necessary and sufficient conditions for a self-adjoint operator on a line related to a general second-order expression to have discrete spectrum are presented in the article [13]. The discreteness of the spectrum of the non-magnetic Schŕ’odinger operator has been studied, for example, in [1, 2, 11, 16]. In the case of a magnetic field, one works in the space of complex functions, which complicates the task. Studies of the magnetic Schrödinger operator were carried out in [3, 6, 7, 10, 14], but no rigorous criteria have been proved for the discreteness of the spectrum of the Schrödinger operator on quantum graphs in a magnetic field. The mathematical modeling of the physical system in this article is based on the theory of quantum graphs. A rigorous proof of the correctness of their use was offered in [15], and the mathematical theory of quantum graphs was treated in [4, 9].

Generalized &#x1D713;-Geraghty-Zamfirescu Contraction Pairs in b-metric Spaces

Abstract: The purpose of this paper is to introduce a class of contractive pairs of mappings satisfying a Zamfirescu-type inequality, but controlled with altering distance functions and with parameters satisfying the so-called Geraghty condition in the framework of b-metric spaces. For this class of mappings we prove the existence of points of coincidence, the convergence and stability of the Jungck, Jungck-Mann and Jungck-Ishikawa iterative processes and the existence and uniqueness of its common fixed points. 1. Motivation In 1922, S. Banach [4] established his famous and fundamental result in the metric fixed point theory as follows: Theorem 1.1.(Banach Contraction Principle) Let (M, d) be a complete metric space and let S : M −→ M be a Banach contraction, that is, S satisfies that there exists α ∈ (0, 1) such that d(Sx, Sy) ≤ αd(x, y) (z1) for all x, y ∈M. Then, S has a unique fixed point in M. Notice that Banach’s contractions are continuous mappings, so, in the spirit to extend the BCP, in 1968, R. Kannan [11] introduced a new class of contractive mappings admitting discontinuous functions, as follows. * Corresponding Author. Received September 13, 2020; revised January 15, 2021; accepted January 19, 2021. 2020 Mathematics Subject Classification: 47H09, 47H10, 47J25.

Baer-Kaplansky Theorem for Modules over Non-commutative Algebras

Abstract: In this paper we investigate the Baer-Kaplansky theorem for module classes on algebras of finite representation types over a field. To do this we construct finite dimensional quiver algebras over any field.

Some Congruences for Andrews’ Partition Function EO(n)

Abstract: Abstract. Recently, Andrews introduced partition functions EO(n) and EO(n) where the function EO(n) denotes the number of partitions of n in which every even part is less than each odd part and the function EO(n) denotes the number of partitions enumerated by EO(n) in which only the largest even part appears an odd number of times. In this paper we obtain some congruences modulo 2, 4, 10 and 20 for the partition function EO(n). We give a simple proof of the first Ramanujan-type congruences EO (10n+ 8) ≡ 0 (mod 5) given by Andrews.

Conservative Upwind Correction Method for Scalar Linear Hyperbolic Equations

Abstract: A conservative scheme for solving scalar hyperbolic equations is presented using a quadrature rule and an ODE solver. This numerical scheme consists of an upwind part, plus a correction part which is derived by introducing a new variable for the given hyperbolic equation. Furthermore, the stability and accuracy of the derived algorithm is shown with numerous computations.

Algorithm of Common Solutions to the Cayley Inclusion and Fixed Point Problems

Abstract: In this paper, we develop an iterative algorithm for obtaining common solutions to the Cayley inclusion problem and the set of fixed points of a non-expansive mapping in Hilbert spaces. A numerical example is given for the justification of our claim.