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Foundations, Volume 2, Issue 1

March 2022 - 22 articles

Cover Story: A plethora of problems from many disciplines can be reduced to solving nonlinear Banach space-valued equations. Most solution methods are of an iterative nature since closed-form solutions are possible only in special cases. We study the semi-local convergence of a three-step Newton-type method for solving nonlinear equations under the classical Lipschitz conditions for first-order derivatives. Earlier studies have used convergence analysis requiring the existence of the sixth derivative not appearing on the method, hence restricting the applicability of the method to operators which are at least six times differentiable. View this paper.
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Articles (22)

  • Article
  • Open Access
5 Citations
10,451 Views
10 Pages

7 February 2022

Vector-valued electromagnetic waves for which the integral of the electric field over time is zero at every location in space were characterized as “usual” by Bessonov several decades ago. Otherwise, they were called “strange”...

  • Feature Paper
  • Review
  • Open Access
3 Citations
2,841 Views
15 Pages

29 January 2022

In the review, based on the analysis of the results published in the works of domestic and foreign researchers, a variant of an unconventional interpretation of the photoluminescence of dispersive media in the energy range of 0.5–3 eV is propos...

  • Feature Paper
  • Article
  • Open Access
5 Citations
2,732 Views
17 Pages

Analytical Study of a ϕ− Fractional Order Quadratic Functional Integral Equation

  • Ahmed M. A. El-Sayed,
  • Hind H. G. Hashem and
  • Shorouk M. Al-Issa

25 January 2022

Quadratic integral equations of fractional order have been studied from different views. Here we shall study the existence of continuous solutions of a ϕ− fractional-orders quadratic functional integral equation, establish some properties...

  • Article
  • Open Access
4 Citations
3,219 Views
16 Pages

21 January 2022

In this paper, we look at the two-point boundary value problem for a finite nabla fractional difference equation with dual non-local boundary conditions. First, we derive the associated Green’s function and some of its properties. Using the Guo...

  • Feature Paper
  • Article
  • Open Access
2,401 Views
11 Pages

On the Semi-Local Convergence of a Fifth-Order Convergent Method for Solving Equations

  • Christopher I. Argyros,
  • Ioannis K. Argyros,
  • Stepan Shakhno and
  • Halyna Yarmola

20 January 2022

We study the semi-local convergence of a three-step Newton-type method for solving nonlinear equations under the classical Lipschitz conditions for first-order derivatives. To develop a convergence analysis, we use the approach of restricted converge...

  • Article
  • Open Access
2 Citations
4,765 Views
12 Pages

Big Rip Scenario in Brans-Dicke Theory

  • Sasmita Kumari Pradhan,
  • Sunil Kumar Tripathy,
  • Zashmir Naik,
  • Dipanjali Behera and
  • Mrutunjaya Bhuyan

17 January 2022

In this work, we present a Big Rip scenario within the framework of the generalized Brans-Dicke (GBD) theory. In the GBD theory, we consider an evolving BD parameter along with a self-interacting potential. An anisotropic background is considered to...

  • Feature Paper
  • Article
  • Open Access
3 Citations
2,404 Views
14 Pages

On the Semi-Local Convergence of a Traub-Type Method for Solving Equations

  • Samundra Regmi,
  • Christopher I. Argyros,
  • Ioannis K. Argyros and
  • Santhosh George

14 January 2022

The celebrated Traub’s method involving Banach space-defined operators is extended. The main feature in this study involves the determination of a subset of the original domain that also contains the Traub iterates. In the smaller domain, the L...

  • Feature Paper
  • Article
  • Open Access
2,779 Views
9 Pages

10 January 2022

Previously published analytical results for the effects of a high-frequency laser field on hydrogen Rydberg atoms demonstrated that the unperturbed elliptical orbit of the Rydberg electron, generally is engaged simultaneously in the precession of the...

  • Article
  • Open Access
11 Citations
3,736 Views
20 Pages

Divergence in the Relativistic Mean Field Formalism: A Case Study of the Ground State Properties of the Decay Chain of 214,216,218U Isotopes

  • Tolulope Majekodunmi Joshua,
  • Nishu Jain,
  • Raj Kumar,
  • Khairul Anwar,
  • Nooraihan Abdullah and
  • Mrutunjaya Bhuyan

9 January 2022

A new α-emitting 214U has been recently observed experimentally. This opens the window to theoretically investigate the ground-state properties of the lightest known even–even neutron deficient 214,216,218U isotopes and to examine α...

  • Feature Paper
  • Article
  • Open Access
8 Citations
4,929 Views
65 Pages

31 December 2021

An alternative to conventional spacetime is proposed and rigorously formulated for nonlocal continuum field theories through the deployment of a fiber bundle-based superspace extension method. We develop, in increasing complexity, the concept of nonl...

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Foundations - ISSN 2673-9321