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Volume 3, Number 2 (2020)
New operators for Fermatean fuzzy sets
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I. Silambarasan
Annals of Communications in Mathematics, Vol. 3 (2) (2020), 116-131
Abstract

 In this paper, we define some new operators[(A@B), (A$B), (A#B), (A∗ B), (A → B)] of Fermatean fuzzy sets. Then we discuss several properties of these operators. Further we prove necessity and possibility operators of Fermatean fuzzy sets and investigates the algebraic properties. Finally, we have identified and proved several of
these properties, particularly those involving the operator A → B defined as Fermatean fuzzy implication with other operators.

I. SILAMBARASAN
DEPARTMENT OF MATHEMATICS, ANNAMALA UNIVERSITY, ANNAMALAINAGAR-608002, TAMILNADU, INDIA.
Email: sksimbuking@gmail.com

On rarely fuzzy e*-continuous functions in the sense of Sostak’s
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E. Elavarasan
Annals of Communications in Mathematics, Vol. 3 (2) (2020), 132-138
Abstract

In this paper, we introduce the concepts of rarely fuzzy e ∗-continuous functions in the sense of Sˇostak’s is introduced. Some interesting properties and characterizations of them are investigated. Also, some applications to fuzzy compact spaces are established.

E. ELAVARASAN
DEPARTMENT OF MATHEMATICS, SHREE RAGHAVENDRA ARTS AND SCIENCE COLLEGE (AFFILIATED TO THIRUVALLUVAR UNIVERSITY), KEEZHAMOONGILADI, CHIDAMBARAM-608102, TAMIL NADU, INDIA.
Email: maths.aras@gmail.com

Study of the global asymptotic stability in nonlinear neutral integro-dynamic
equations

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Abdelouaheb Ardjouni
Annals of Communications in Mathematics, Vol. 3 (2) (2020), 139-151
Abstract

The main purpose of this paper is to establish the global asymptotic stability of the zero solution of a class of nonlinear neutral integro-dynamic equations in C1 rd. Global asymptotic stability results are based on the Banach fixed point theorem. The results obtained here extend the work of Huang, Zhao and Liu [19].

ABDELOUAHEB ARDJOUNI
DEPARTMENT OF MATHEMATICS AND INFORMATICS, UNIVERSITY OF SOUK AHRAS, P.O. BOX 1553,
SOUK AHRAS, 41000, ALGERIA
APPLIED MATHEMATICS LAB, FACULTY OF SCIENCES, DEPARTMENT OF MATHEMATICS, UNIVERSITY OF ANNABA, P.O. BOX 12, ANNABA 23000, ALGERIA
Email: abd ardjouni@yahoo.fr

Generalized U-H stability of cubic mappings
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V. Govindan, S. Pinelas and N. Gunasekaran
Annals of Communications in Mathematics, Vol. 3 (2) (2020), 152-157
Abstract

In this work, we investigate the generalized Ulam-Hyers stability of the ωdimensional cubic functional equation

where ω ≥ 4, in Banach spaces using direct and fixed point methods.

DEPARTMENT OF MATHEMATICS, SRI VIDYA MANDIR ARTS & SCIENCE COLLEGE KATTERI, UTHANGARAI, TAMILNADU, INDIA-636902
Email: govindoviya@gmail.com

DEPARTMENTO DE CIE NCIAS EXATAS ENGENHARIA, ACADEMIA MILITAR, PORTUGAL.
Email: sandra.pinelas@gmail.com

DEPARTMENT OF MATHEMATICS, SHIBAURA INSTITUTE OF TECHNOLOGY, JAPAN.
Email: gunasmaths@gmail.com

Hesitant anti-intuitionistic fuzzy soft commutative ideals of BCK-algebras
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G. Muhiuddin, A. Mahboob and M. Balamurugan
Annals of Communications in Mathematics, Vol. 3 (2) (2020), 158-170
Abstract

In this paper, the notions of hesitant anti-intuitionistic fuzzy soft BCI-commutative ideals of BCI-algebras and hesitant anti-intuitionistic fuzzy soft subcommutative ideals of BCK-algebras are introduced and their related properties are investigate. Relations between a hesitant anti-intuitionistic fuzzy soft ideals and hesitant anti-intuitionistic fuzzy soft BCI-commutative ideals are discussed. Conditions for a hesitant anti-intuitionistic fuzzy soft ideal to be a hesitant anti-intuitionistic fuzzy soft BCIcommutative ideal are provided. Finally, it is proved that a hesitant anti-intuitionistic fuzzy soft p-ideal is a hesitant anti-intuitionistic fuzzy soft sub-commutative ideal in a BCKalgebra.

G. MUHIUDDIN
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF TABUK, TABUK 71491, SAUDI ARABIA.
Email: chishtygm@gmail.com

AHSAN MAHBOOB
MADANAPALLE INSTITUTE OF TECHNOLOGY & SCIENCE, ANGALLU, MADANAPALLE 517325, INDIA
Email: khanahsan56@gmail.com

M. BALAMURUGAN
DEPARTMENT OF MATHEMATICS, SRI VIDYA MANDIR ARTS AND SCIENCE COLLEGE, UTHANGARAI 636902, TAMILNADU, INDIA.
Email: mbalamurugan@gmail.com.

Cube sum labeling of graphs
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V. Govindan, S. Pinelas and S. Dhivya
Annals of Communications in Mathematics, Vol. 3 (2) (2020), 171-176
Abstract

 Here, we define a cube sum labeling and cube sum graph. Let G be a (p, q) graph. G is said to be a cube sum graph if there exist a bijection f : V (G) → {0, 1, . . . , p − 1} such that the induced function f ∗ : E(G) → N given by

are all distinct. In this paper, we developed the concept of cube sum labeling of some family of graphs like paths, cycle, stars, wheel graph, fan graphs are discussed in this paper.

ASSISTANT PROFESSOR, DEPARTMENT OF MATHEMATICS, SRI VIDYA MANDIR ARTS & SCIENCE COLLEGE,KATTERI, UTHANGARAI(TK), KRISHNAGIRI(DT),TAMILNADU,INDIA. THANJAVUR, INDIA.
Email:  govindoviya@gmail.com

DEPARTMENTO DE CIE NCIAS EXATAS E ENGENHARIA, ACADEMIA MILITAR, PORTUGAL
Email: sandra.pinelas@gmail.com

RESEARCH SCHOLAR, DEPARTMENT OF MATHEMATICS, SRI VIDYA MANDIR ARTS & SCIENCE COLLEGE,KATTERI, UTHANGARAI(TK), KRISHNAGIRI(DT),TAMILNADU,INDIA.
Email: dhivyasundar.msc@gmail.com

Ulam stability for finite variable quadratic functional equation in Banach
algebra

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K. Tamilvanan, G. Balasubramanian and K. Loganathan
Annals of Communications in Mathematics, Vol. 3 (2) (2020), 177-184
Abstract

In this paper, we determine some stability results concerning the quartic functional equation as of the form

K. TAMILVANAN
GOVERNMENT ARTS COLLEGE FOR MEN, KRISHNAGIRI-635 001, TAMILNADU, INDIA.
Email: tamiltamilk7@gmail.com

K. LOGANATHAN
RESEARCH AND DEVELOPMENT WING, CLOUDIN SOFTWARE TECH LABS PVT LTD., COIMBATORE, TAMILNADU, INDIA.
Email: loganathankaruppusamy304@gmail.com (Corresponding author)

G. BALASUBRAMANIAN
GOVERNMENT ARTS COLLEGE FOR MEN, KRISHNAGIRI-635 001, TAMILNADU, INDIA.
Email: gbs geetha@yahoo.com

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