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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)

  • Review
  • Open Access
18 Citations
9,784 Views
30 Pages

21 March 2022

There is little doubt that life’s origin followed from the known physical and chemical laws of Nature. The most general scientific framework incorporating the laws of Nature and applicable to most known processes to good approximation, is that...

  • Article
  • Open Access
1 Citations
2,713 Views
10 Pages

11 March 2022

The objective of this research is to obtain some fractional integral formulas concerning products of the generalized Mittag–Leffler function and two H-functions. The resulting integral formulas are described in terms of the H-function of severa...

  • Article
  • Open Access
3 Citations
2,306 Views
8 Pages

A coupled system of Hilfer fractional differential inclusions with nonlocal integral boundary conditions is considered. An existence result is established when the set-valued maps have non-convex values. We treat the case when the set-valued maps are...

  • Article
  • Open Access
4 Citations
4,758 Views
39 Pages

We utilize relativistic quantum mechanics to develop general quantum field-theoretic foundations suitable for understanding, analyzing, and designing generic quantum antennas for potential use in secure quantum communication systems and other applica...

  • Feature Paper
  • Article
  • Open Access
2 Citations
2,297 Views
9 Pages

On the Local Convergence of a (p + 1)-Step Method of Order 2p + 1 for Solving Equations

  • Janak Raj Sharma,
  • Ioannis K. Argyros,
  • Harmandeep Singh and
  • Michael I. Argyros

20 February 2022

The local convergence of a generalized (p+1)-step iterative method of order 2p+1 is established in order to estimate the locally unique solutions of nonlinear equations in the Banach spaces. In earlier studies, convergence analysis for the given iter...

  • Feature Paper
  • Article
  • Open Access
2 Citations
2,207 Views
8 Pages

On the Semi-Local Convergence of a Jarratt-Type Family Schemes for Solving Equations

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

17 February 2022

We study semi-local convergence of two-step Jarratt-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 convergence regi...

  • Communication
  • Open Access
1 Citations
2,498 Views
6 Pages

14 February 2022

We analyze Molecular Hydrogen Ions (MHIs) formed by collisions of low-energy protons with the Second Flavor of Hydrogen Atoms SFHA, whose existence was previously proven by two kinds of atomic experiments and also evidenced by two kinds of astrophysi...

  • Article
  • Open Access
3 Citations
2,809 Views
9 Pages

12 February 2022

In the framework of the effective mass approximation, negative and positive trions, exciton, and biexciton states are investigated in strongly prolate ellipsoidal quantum dots by the variational method. Since the ellipsoidal quantum dot has a prolate...

  • Article
  • Open Access
6 Citations
2,889 Views
9 Pages

7 February 2022

In this paper, fractional Lyapunov functions for epidemic models are introduced and the concept of Mittag-Leffler stability is applied. The global stability of the epidemic model at an equilibrium state is established.

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Foundations - ISSN 2673-9321