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2024

Vol 2, No 2 (2024)

Vol 2, No 1 (2024)

2023

Vol 1, No 1 (2023)

Featured Articles

Why the big bang never happened

If general relativity is correct, then the origin of the universe is a simple mathematical problem. The Friedmann equation in cosmology is a well-structured ordinary diﬀerential equation, and the global properties of its solutions can be qualitatively analyzed by the phase-trajectory method. In this paper we show that the total energy density of matter in the universe is positive, and the total pressure near the Big Bang is negative. By analyzing the global properties of the solutions to the Friedmann equation according to these two conditions of state functions, we ﬁnd that the Big Bang is impossible, and the space must be a closed 3-dimensional sphere, the cosmological constant is likely to be zero, and the evolution of the universe should be cyclic. The analysis and the proof are simple and straight forward, therefore these conclusions should be reliable.

Fermat surfaces and hypercubes

Fermat’s last theorem appears not as a unique property of natural numbers but as the bottom line of extended possible issues involving larger dimensions and powers when observed from a natural vector space viewpoint. The fabric of this general Fermat’s theorem structure consists of a well-defined set of vectors associated with dimensional vector spaces and the Minkowski norms one can define there. Here, a special vector set is studied and named a Fermat surface. Besides, a connection between Fermat surfaces and hypercubes is unveiled.

On “A new three-step fixed point iteration scheme with strong convergence and applications”

Arif Rafiq

Article ID: 2918
Vol 3, Issue 1, 2025

DOI: https://doi.org/10.54517/mss2918

Received: 31 August 2024; Accepted: 12 November 2024; Available online: 19 November 2024; Issue release: Vol 3, No 1

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Abstract

This note delves into the convergence analysis of several iterative methods and elucidates their behaviors. Furthermore, we demonstrate that the findings presented in “A new three-step fixed point iteration scheme with strong convergence and applications” are not entirely novel. In particular, some of the results either overlap with or restate previously established methods without introducing significant innovations.

Keywords

algorithms; iterative methods; convergence order

References

1. Traub JF. Iterative methods for the solution of equations. Prentice-Hall Englewood Cliffs; 1964.

2. Kang SM, Rafiq A, Kwun YC. A new second-order iteration method for solving nonlinear equations. Abst. Appl. Anal. 2013; 1.

3. Sharma P, Ramos H, Behl R, Kanwar V. A new three-step fixed point iteration scheme with strong convergence and applications. J. Comput. Appl. Math. 2023; 430: 115–242.

4. Mann WR. Mean value methods in iteration. Proc. Amer. Math. Soc. 1953; 4: 506–610.

5. Ishikawa S. Fixed point by a new iteration method. Proc. Amer. Math. Soc. 1974; 4(1): 147–150.

6. Noor MA. Some approximation schemes for general variational inequalities. J. Math. Anal. Appl. 2000; 251: 217–229.

7. Kirk WA. On successive approximations for nonexpansive mappings in Banach spaces. Glasg. Math. J. 1971; 12: 6–9.

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Prof. Youssri Hassan Youssri

Cairo University, Egypt

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News & Announcements

2024-09-20

Highly Read Article Recommendation

Since the journal launch in 2023, we have been proud to publish a plethora of insightful findings in the realms of mathematics and systems science....

2024-07-10

Meeting our Editor-in-Chief and Associate Editor

It is with great pride that we introduce Prof. Youssri Hassan Youssri and Prof. Ali Akgül, who are the Editor-in-Chief and Associate Editor of our esteemed journal.

2024-01-05

Articles in the First Issue of Volume 1 - Now Available Online

We are delighted to announce that the articles in the first issue of Volume 1 of Mathematics and Systems Science is now live and accessible online.

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