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How to cite: Colak, E. Preprints , Colak, E. Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Close menu.

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As it is known, Neutrosophic theory, which brings a new breath to daily life and complex scientific studies which we encounter with many uncertainties, is a rapidly developing field with many new study subjects. Thus, researchers show great interest in this philosophical approach and try to transfer related topics to this field quickly. As a result, it is thought that the selected convergence type is suitable for the Neutrosophic normed space structure and is a guide for new convergence types. Ali, G. Multiattribute decision-making under Fermatean fuzzy bipolar soft framework. Granular Computing, 7 2 , Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20 1 , Sur la convergence statistique. Colloquium Mathematicae, 2 , Finite-dimensional fuzzy normed linear space. Fuzzy Sets and Systems, 48 2 , Control of chaos: methods and applications in engineering.

Dagdeviren, S.

This work is concerned with several important different types of convergence that will be described on neutrosophic normed spaces. In the study, arithmetic convergence was combined with different types of statistical convergence and then integrated into the structure of neutrosophic spaces established through the membership function. For this purpose, in the neutrosophic normed space, firstly, the concepts of arithmetic convergence and arithmetic statistical convergence are given, then some important definitions that can be established with lacunary sequences and ideal structures and some relationships between convergent sequences in this sense are examined. Furthermore, new convergence definitions were established by evaluating lambda sequences together with arithmetic convergence and statistical convergence with the help of neutrosophic normed space structure properties. Finally, with the help of the definition of graduated convergence, the inclusion relation between the two set is given.

As it is known, Neutrosophic theory, which brings a new breath to daily life and complex scientific studies which we encounter with many uncertainties, is a rapidly developing field with many new study subjects. Thus, researchers show great interest in this philosophical approach and try to transfer related topics to this field quickly. As a result, it is thought that the selected convergence type is suitable for the Neutrosophic normed space structure and is a guide for new convergence types. English Turkish English. Research Article. Create Research Close. References Ali, G. Multiattribute decision-making under Fermatean fuzzy bipolar soft framework. Granular Computing, 7 2 ,

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Ideal convergence of sequences in neutrosophic normed spaces. Lambda-statistical convergence. Chesnut, J. Burgos, F. Alsubie, N. Edmonds, J. AIMS Mathematics, 7 8 , Xin, M. Signal Process. Sur la convergence statistique. Karami, H. Smarandache, Taylor series approximation to solve neutrosophic multiobjective programming problem, Neutrosophic Sets Syst. Sady, H.

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Significant contribution. Temiz, A new evaluation model for service quality of healthcare systems based on AHP and information axiom, J. Nazmiye Gonul Bilgin. Research article. Communications in Advanced Mathematical Sciences, 5 1 , Riaz, Y. Some new type of lacunary statistically convergent sequences in neutrosophic normed space. Woldesilassie, T. How to cite: Colak, E. Xin, M.