449 447

Title

A Study of Neutrosophic Real Analysis by Using the One-Dimensional Geometric AH-Isometry

  Mohammad Abobala 1 * ,   Mohamed Bisher Zeina 2

1  Faculty of Science, Tishreen University, Lattakia, Syria
    (mohammadabobala777@gmail.com)

2  Department of Mathematical Statistics, Faculty of Science, University of Aleppo, Aleppo, Syria
    (bisher.zeina@gmail.com)


Doi   :   https://doi.org/10.54216/GJMSA.030103

Received: October 09, 2022 Accepted: January 08, 2023

Abstract :

The objective of this paper is to study and define the neutrosophic real functions with one neutrosophic variable depending on the geometric isometry (AH-Isometry), with a lot of concepts from real analysis including continuality, differentiability, integrability. We have presented the formal forms of different popular functions in neutrosophic environment like logarithmic function, exponential function, trigonometric functions. Rising neutrosophic numbers to any power is well defined including rising to neutrosophic powers.

Keywords :

Neutrosophic real analysis; AH-isometry; Integration; Differentiation; Continuity.

References :

[1]  Abobala,  M.,  "AH-Subspaces  in  Neutrosophic  Vector  Spaces",  International  Journal  of  Neutrosophic 

Science, Vol. 6 , pp. 80-86. 2020.

[2]  Abobala,  M.,.  "A  Study  of  AH-Substructures  in  n-Refined  Neutrosophic  Vector  Spaces",  International 

Journal of Neutrosophic Science", Vol. 9, pp.74-85. 2020.

[3]  Alhamido, R., and Abobala, M., "AH-Substructures in Neutrosophic Modules", International Journal of

Neutrosophic Science, Vol. 7, pp. 79-86 . 2020.

[4]  Smarandache,  F.,  "  A  Unifying  Field  in  Logics:  Neutrosophic  Logic,  Neutrosophy,  Neutrosophic  Set, 

Neutrosophic Probability", American Research Press. Rehoboth, 2003.

[5]  Suresh,  R.,  and  S.  Palaniammal,.  "Neutrosophic  Weakly  Generalized  open  and  Closed  Sets", 

Neutrosophic Sets and Systems, Vol. 33, pp. 67-77,. 2020.

[6]  Olgun,  N.,  and   Hatip,  A.,   "The  Effect  Of  The  Neutrosophic  Logic  On  The  Decision  Making,  in 

Quadruple Neutrosophic Theory And Applications", Belgium, EU, Pons Editions Brussels,pp. 238-253. 

2020.

[7]  Abobala, M., "Classical Homomorphisms Between n-refined Neutrosophic Rings", International Journal 

of Neutrosophic Science", Vol. 7, pp. 74-78. 2020. 

[8]  Smarandache, F., and Abobala, M., n-Refined neutrosophic Rings, International Journal of Neutrosophic 

Science, Vol. 5 , pp. 83-90, 2020.

[9]  Abobala, M.,  On Some Special Substructures of Neutrosophic Rings and Their Properties, International 

Journal of Neutrosophic Science", Vol. 4 , pp. 72-81, 2020.

[10]  Abobala, M., "On Some Special Substructures of Refined Neutrosophic Rings",  International Journal of 

Neutrosophic Science, Vol. 5, pp. 59-66. 2020.

[11]  Sankari,  H., and Abobala, M.," AH-Homomorphisms In neutrosophic Rings and Refined Neutrosophic 

Rings", Neutrosophic Sets and Systems, Vol. 38, pp. 101-112, 2020.

[12]  Smarandache,  F.,  and  Kandasamy,  V.W.B.,  "  Finite  Neutrosophic  Complex  Numbers",·Source:  arXiv. 

2011.

[13]  Agboola, A.A.A,.Akwu, A.D,. and Oyebo, Y.T., " Neutrosophic Groups and Subgroups", International .J 

.Math. Combin, Vol. 3, pp. 1-9. 2012.

[14]  Smarandache, F., " n-Valued Refined Neutrosophic Logic and Its Applications in Physics", Progress in 

Physics, 143-146, Vol. 4, 2013.

[15]  Adeleke,  E.O.,  Agboola,  A.A.A.,and  Smarandache,  F.,   "Refined  Neutrosophic  Rings  I",  International 

Journal of Neutrosophic Science, Vol. 2(2), pp. 77-81. 2020.

[16]  Adeleke, E.O., Agboola, A.A.A., and Smarandache, F., "Refined Neutrosophic Rings II",  International 

Journal of Neutrosophic Science, Vol. 2(2), pp. 89-94. 2020.

[17]  Abobala,  M.,  On  Refined  Neutrosophic  Matrices  and  Their  Applications  In  Refined  Neutrosophic 

Algebraic Equations, Journal Of Mathematics, Hindawi, 2021

[18]  Giorgio, N, Mehmood, A., and Broumi, S.," Single Valued neutrosophic Filter", International Journal of 

Neutrosophic Science, Vol. 6, 2020.

[19]  Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings", 

Neutrosophic Sets and Systems, Vol. 45, 2021. 

[20]  Milles,  S,  Barakat,  M,  and  Latrech,  A.,  "  Completeness  and  Compactness  In  Standard  Single  Valued 

neutrosophic Metric Spaces", International Journal of Neutrosophic Science, Vol.12 , 2021.

[21]  Abobala,  M.,  "On  Some  Algebraic  Properties  of  n-Refined  Neutrosophic  Elements  and  n-Refined 

Neutrosophic Linear Equations", Mathematical Problems in Engineering, Hindawi, 2021

[22]   Kandasamy V, Smarandache F., and Kandasamy I., Special Fuzzy Matrices for Social Scientists . Printed 

in the United States of America,2007, book, 99 pages.

[23]   Khaled,  H.,  and  Younus,  A.,  and  Mohammad,  A.,  "  The  Rectangle  Neutrosophic  Fuzzy  Matrices", 

Faculty of Education Journal Vol. 15, 2019. (Arabic version).

[24]   F. Smarandache, Neutrosophic Theory and Applications, Le Quy Don Technical University, Faculty of 

Information technology, Hanoi, Vietnam, 17

th

May 2016.

[25]  Ibrahim,  M.,  and  Abobala,  M.,  "An  Introduction  To  Refined  Neutrosophic  Number  Theory", 

Neutrosophic Sets and Systems, Vol. 45, 2021.

[26]  Ibrahim,  M.A.,  Agboola,  A.A.A,  Badmus,  B.S.,  and  Akinleye,  S.A.,  "On  refined  Neutrosophic  Vector 

Spaces II", International Journal of Neutrosophic Science, Vol. 9, pp. 22-36. 2020.

[27]  Abobala, M, "n-Cyclic Refined Neutrosophic Algebraic Systems Of Sub-Indeterminacies, An Application 

To Rings and Modules", International Journal of Neutrosophic Science, Vol. 12, pp. 81-95 . 2020.

[28]  Smarandache, F., "Neutrosophic Set a Generalization of the Intuitionistic Fuzzy Sets", Inter. J. Pure Appl. 

 

Math., pp. 287-297. 2005. 

[29]   Merkepci, H., and Abobala, M., " The Application of AH-isometry In The Study Of Neutrosophic Conic 

Sections", Galoitica Journal Of Mathematical Structure And Applications, Vol.2, 2022.

[30]  Aswad,  F,  M.,  "  A  Study  of  Neutrosophic  Complex  Number  and  Applications",  Neutrosophic 

Knowledge, Vol. 1, 2020.

[31]   Aswad. F, M., " A Study of neutrosophic Bi Matrix", Neutrosophic Knowledge, Vol. 2, 2021.

[32]   Aswad,  M.,  "  A  Study  of  The  Integration  Of  Neutrosophic  Thick  Function",  International  journal  of 

neutrosophic Science, 2020. 

[33]   Ali, R, "Neutrosophic Matrices and their Properties", Hal- Archives, 2021. 

[34]   Abobala,  M.,  and  Hatip,  A.,  "An  Algebraic  Approach  to  Neutrosophic  Euclidean  Geometry", 

Neutrosophic Sets and Systems, Vol. 43, 2021.

[35]   Aswad, M., " A Study Of neutrosophic Differential Equation By using A Neutrosophic Thick Function", 

neutrosophic knowledge, Vol. 1, 2020.

[36]  Olgun,  N.,  Hatip,  A.,  Bal,  M.,  and  Abobala,  M.,  "  A  Novel  Approach  To  Necessary  and  Sufficient 

Conditions  For  The  Diagonalization  of  Refined  Neutrosophic  Matrices",  International  Journal  of 

Neutrosophic Science, Vol. 16, pp. 72-79, 2021.

[37]  Khaled,  H.,  Smarandache,  F.,  and  Essa,  A.,  "A  Neutrosophic  Binomial  Factorial  Theorem  With  Their 

Refrains", Neutrosophic Sets and Systems, Vol. 14, 2016.

[38]  Zeina, M. B., and Hatip, A., "Neutrosophic Random Variables ", Neutrosophic Sets and Systems, Vol. 39 

, 2021.

[39]  Zeina, M. B., "Erlang  Service Queueing Model with Neutrosophic Parameters", International Journal of 

Neutrosophic Science, Vol. 6 ,2020.

[40]  Zeina,  M.  B.,  "Neutrosophic  Event-Based  Queueing  Model",  International  Journal  of  Neutrosophic 

Science, Vol. 6 , 2020.

[41]  Ali,  R.,  "A  Short  Note  On  The  Solution  of  n-Refined  Neutrosophic  Linear  Diophantine  Equations", 

International Journal Of Neutrosophic Science, Vol. 15, 2021.

[42]  Hajjari,  A.,  and  Ali,  R.,  "  A  Contribution  To  Kothe's  Conjecture  In  Refined  Neutrosophic  Rings", 

International Journal of Neutrosophic Science", Vol. 16, 2021.

[43]  Merkepci, M,; Sarkis, M. An Application of Pythagorean Circles in  Cryptography and Some Ideas for 

Future Non Classical  Systems. Galoitica Journal of Mathematical Structures and Applications  2022,  2, 

28-30, doi: 10.54216/GJMSA.020205.

[44]   Merkepci,  M.,  and  Ali,  R.,  "  A  Study  of  Some  Neutrosophic  Algebraic  Games  and  Their  Winning 

Stratigies", Galoitica Journal Of Mathematical Structure And Applications, Vol.2, 2022.

[45]  Merkepci, H., and Ahmad, K., " On The Conditions Of Imperfect Neutrosophic Duplets and Imperfect 

 

Neutrosophic Triplets", Galoitica Journal Of Mathematical Structure And Applications, Vol.2, 2022.

 


Cite this Article as :
Style #
MLA Mohammad Abobala, Mohamed Bisher Zeina. "A Study of Neutrosophic Real Analysis by Using the One-Dimensional Geometric AH-Isometry." Galoitica: Journal of Mathematical Structures and Applications, Vol. 3, No. 1, 2023 ,PP. 18-24 (Doi   :  https://doi.org/10.54216/GJMSA.030103)
APA Mohammad Abobala, Mohamed Bisher Zeina. (2023). A Study of Neutrosophic Real Analysis by Using the One-Dimensional Geometric AH-Isometry. Journal of Galoitica: Journal of Mathematical Structures and Applications, 3 ( 1 ), 18-24 (Doi   :  https://doi.org/10.54216/GJMSA.030103)
Chicago Mohammad Abobala, Mohamed Bisher Zeina. "A Study of Neutrosophic Real Analysis by Using the One-Dimensional Geometric AH-Isometry." Journal of Galoitica: Journal of Mathematical Structures and Applications, 3 no. 1 (2023): 18-24 (Doi   :  https://doi.org/10.54216/GJMSA.030103)
Harvard Mohammad Abobala, Mohamed Bisher Zeina. (2023). A Study of Neutrosophic Real Analysis by Using the One-Dimensional Geometric AH-Isometry. Journal of Galoitica: Journal of Mathematical Structures and Applications, 3 ( 1 ), 18-24 (Doi   :  https://doi.org/10.54216/GJMSA.030103)
Vancouver Mohammad Abobala, Mohamed Bisher Zeina. A Study of Neutrosophic Real Analysis by Using the One-Dimensional Geometric AH-Isometry. Journal of Galoitica: Journal of Mathematical Structures and Applications, (2023); 3 ( 1 ): 18-24 (Doi   :  https://doi.org/10.54216/GJMSA.030103)
IEEE Mohammad Abobala, Mohamed Bisher Zeina, A Study of Neutrosophic Real Analysis by Using the One-Dimensional Geometric AH-Isometry, Journal of Galoitica: Journal of Mathematical Structures and Applications, Vol. 3 , No. 1 , (2023) : 18-24 (Doi   :  https://doi.org/10.54216/GJMSA.030103)