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2024

Vol 2, No 2 (2024)

Vol 2, No 1 (2024)

2023

Vol 1, No 1 (2023)

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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.

Note on “stability and data dependence results for jungck-type iteration scheme”

Arif Rafiq

Article ID: 2919
Vol 2, Issue 1, 2024

DOI: https://doi.org/10.54517/mss2919

Received: 29 May 2024; Accepted: 20 June 2024; Available online: 27 June 2024; Issue release: 30 June 2024

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Abstract

This note reviews the iterative methods introduced in “Stability and Data De- pendence Results for Jungck-Type Iteration Scheme”. It has been observed that these methods are not entirely new to a significant extent, as they bear resemblance to pre- viously established approaches. Additionally, the primary iterative method proposed in the paper lacks efficiency, particularly when compared to more advanced or well- known methods. As a result, while the methods may offer some value, they do not represent a significant breakthrough in iterative techniques.

Keywords

algorithms; iteration methods; convergence order

References

1. Kang SM, Rafiq A, Kwun YC. A new second-order iteration method for solving nonlinear equations. Abstract and Applied Analysis. 2013; (SI07): 1–4

2. Rafiq A, Tanveer M, Kang SM, et al. The modified Jungck Mann and modified Jungck Ishikawa iteration schemes for Zamfirescu operators. International Journal of Pure and Applied Mathematics. 2015; 2(102): 357–382.

3. Singh SL, Bhatnagar C, Mishra SN. Stability of Jungck-type itera-tive procedures. Int. J. Math. Math. Sci. 2005; 19: 3035–3043.

4. Kirk WA. On successive approximations for nonexpansive mappings in Banach spaces. Glasgow Mathematical Journal. 1971; 12: 6–9.

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

6. Sharma P, Argyros IK, Behl R, Kanwar V. Stability and data dependence results for Jungck-Type iteration scheme. Contemporary Mathematics. 2024; 5(1): 743–760.

7. Jungck G. Commuting mappings and fixed points. The American Mathematical Monthly. 1976; 83(4): 261–263.

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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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