On the Ideal Convergent Sequences in Fuzzy Normed Space

Altaweel, Nifeen Hussain; Rashid, M. H. M.; Albalawi, Olayan; Alshehri, Maryam G.; Eljaneid, Nidal H. E.; Albalawi, Razan Kamel Ahmed

doi:10.3390/sym15040936

Cited by 4 publications

(1 citation statement)

References 17 publications

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“…Sahiner and Tripathy [16] subsequently applied the notion of I-convergence to triple sequences in metric spaces, attracting considerable attention from mathematicians across various disciplines. For instance, Altaweel et al [18] adapted this theory to the fuzzy metric space, while Kočinac and Rashid [9] expanded it to encompass the probabilistic metric space. Furthermore, Rashid and Kočinac and Rashid [10] delved into the investigation of the ideal of convergence within the framework of fuzzy 2-normed space.…”

Section: Introductionmentioning

confidence: 99%

Regarding the Ideal Convergence of Triple Sequences in Random 2-Normed Spaces

Bani-Ahmad,

Rashid

2023

Symmetry

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In our ongoing study, we explore the concepts of I3-Cauchy and I3-Cauchy for triple sequences in the context of random 2-normed spaces (RTNS). Moreover, we introduce and analyze the notions of I3-convergence, I3-convergence, I3-limit points, and I3-cluster points for random 2-normed triple sequences. Significantly, we establish a notable finding that elucidates the connection between I3-convergence and I3-convergence within the framework of random 2-normed spaces, highlighting their interrelation. Additionally, we provide an illuminating example that demonstrates how I3-convergence in a random 2-normed space might not necessarily imply I3-convergence. Our observations underscore the importance of condition (AP3) when examining summability using ideals. Furthermore, we thoroughly investigate the relationship between the properties (AP) and (AP3), illustrating through an example how the latter represents a less strict condition compared to the former.

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Section: Introductionmentioning

confidence: 99%

Regarding the Ideal Convergence of Triple Sequences in Random 2-Normed Spaces

Bani-Ahmad,

Rashid

2023

Symmetry

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Analysis of Teaching Capacity Building of College Teachers’ Innovation and Entrepreneurship Education in the Context of Big Data

Ruan,

Shi,

Ruan

2024

Applied Mathematics and Nonlinear Sciences

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Innovation and entrepreneurship education teaching is an important driving force to stimulate the innovation ability of college and university students and to improve them, which puts forward a major test for the teaching ability of college and university teachers as a key part of teaching. This paper analyzes the current situation of the teaching ability of college teachers in innovative entrepreneurship education teaching through a questionnaire survey. It constructs the evaluation index system of innovation and entrepreneurship teaching ability of college teachers, combines the gray correlation analysis method to determine the weight of each index in the system, and finally successfully constructs the rating system of innovation and entrepreneurship teaching ability of college teachers. Regression analysis and gray correlation methods are used to explore the influencing factors of college teachers’ ability to teach innovation and entrepreneurship. It was found that five factors, such as school type, education, and title, had a significant impact on college teachers’ innovation and entrepreneurial teaching ability. The correlation between participation in innovation and entrepreneurship training and the innovation and entrepreneurship teaching ability of college teachers in the gray correlation calculation is 0.758, which has a significant effect on teachers’ innovation and entrepreneurship teaching ability.

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A Framework for I*-Statistical Convergence of Fuzzy Numbers

Tanushri,

Ahmad,

Esi

2024

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In this study, we investigate the concept of I*-statistical convergence for sequences of fuzzy numbers. We establish several theorems that provide a comprehensive understanding of this notion, including the uniqueness of limits, the relationship between I*-statistical convergence and classical convergence, and the algebraic properties of I*-statistically convergent sequences. We also introduce the concept of I*-statistical pre-Cauchy and I*-statistical Cauchy sequences and explore its connection to I*-statistical convergence. Our results show that every I*-statistically convergent sequence is I*-statistically pre-Cauchy, but the converse is not necessarily true. Furthermore, we provide a sufficient condition for an I*-statistically pre-Cauchy sequence to be I*-statistically convergent, which involves the concept of I*−liminf.

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On the Ideal Convergent Sequences in Fuzzy Normed Space

Cited by 4 publications

References 17 publications

Regarding the Ideal Convergence of Triple Sequences in Random 2-Normed Spaces

Regarding the Ideal Convergence of Triple Sequences in Random 2-Normed Spaces

Analysis of Teaching Capacity Building of College Teachers’ Innovation and Entrepreneurship Education in the Context of Big Data

A Framework for I*-Statistical Convergence of Fuzzy Numbers

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