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Volume 4, Number 1 (2021)
Existence of solutions for Hadamard fractional differential equations in
Banach spaces

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Abdelouaheb Ardjouni
Annals of Communications in Mathematics, Vol. 4 (1) (2021), 1-9
Abstract

 In this work, we investigate the existence of solutions for Hadamard fractional differential equations with integral boundary conditions in a Banach space. We will make use the measure of noncompactness and the Monch fixed point theorem to prove the ¨ main results. An example is given to illustrate our results.

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

Weakly irreducible UP-filters of meet-commutative UP-algebras
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Daniel A. Romano
Annals of Communications in Mathematics, Vol. 4 (1) (2021), 10-16
Abstract

 The concept of meet-commutative UP-algebras was introduced in 2016 by Sawika et al. Muhiuddin et al. introduced in 2021 the concept of prime UP-filter (of the first kind) and irreducible UP-filter in meet-commutative UP-algebras. Also, it has been shown that any prime UP-filter in such algebras is irreducible. In this paper, we introduce the concept of weakly irreducible UP-filters in such algebras and show that the prime UPfilter is between this and the irreducible UP-filter. Also, we show the possibility that each irreducible UP-filter is a weakly irreducible UP-filter

INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE
KORDUNASKA ˇ STREET, 78000 BANJA LUKA, BOSNIA AND HERZEGOVINA
Email: bato49@hotmail.com

On various almost ideals of semirings
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M. Palanikumar and K. Arulmozhi
Annals of Communications in Mathematics, Vol. 4 (1) (2021), 17-25
Abstract

In this paper, we study various almost ideals (shortly A -ideals), quasi A – ideals, bi quasi A -ideals, tri A -ideals and tri quasi A -ideals in semiring and give some characterizations. Some relevant counter examples are also indicated. We develop the implications ideal =⇒ quasi ideal =⇒ bi quasi ideal =⇒ tri quasi ideal =⇒ tri quasi A -ideal =⇒ bi quasi A -ideal =⇒ bi A -ideal =⇒ quasi A -ideal =⇒ A -ideal and reverse implications do not holds with examples. We show that the union of A -ideals (bi A -ideals, quasi A -ideals, bi quasi A -ideals) is a A -ideal (bi A -ideal, quasi A -ideal, bi quasi A -ideal) in semiring.

M. PALANIKUMAR
ANNAMALAI UNIVERSITY, DEPARTMENT OF MATHEMATICS, CHIDAMBARAM, 608002, INDIA
Email: palanimaths86@gmail.com

K. ARULMOZHI
ANNAMALAI UNIVERSITY, DEPARTMENT OF MATHEMATICS, CHIDAMBARAM, 608002, INDIA
Email: arulmozhiems@gmail.com

e⋆-connectedness in intuitionistic fuzzy topological spaces
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S. Sivasangiri, R. Balakumar and G. Saravanakumar
Annals of Communications in Mathematics, Vol. 4 (1) (2021), 26-34
Abstract

In this paper the concept of types of intuitionistic fuzzy e ?-connected and intuitionistic fuzzy e ?-extremally disconnected in intuitionistic fuzzy topological spaces are introduced and studied. Here we introduce the concepts of intuitionistic fuzzy e ?C5- connectedness, intuitionistic fuzzy e ?CS-connectedness, intuitionistic fuzzy e ?CM-connectedness, intuitionistic fuzzy e ?-strongly connectedness, intuitionistic fuzzy e ?-super connectedness, intuitionistic fuzzy e ?Ci-connectedness (i = 1, 2, 3, 4), and obtain several properties and some characterizations concerning connectedness in these spaces.

S. SIVASANGARI
DEPARTMENT OF MATHEMATICS, PONNAIYAH RAMAJAYAM INSTITUTE OF SCIENCE & TECHNOLOGY (PRIST)(INSTITUTION DEEMED TO BE UNIVERSITY), THANJAVUR-613403, TAMILNADU
Email: sivasangarimaths2020@gmail.com

R. BALAKUMAR
DEPARTMENT OF MATHEMATICS, PONNAIYAH RAMAJAYAM INSTITUTE OF SCIENCE & TECHNOLOGY (PRIST)(INSTITUTION DEEMED TO BE UNIVERSITY), THANJAVUR-613403, TAMILNADU
Email: balaphdmaths@gmail.com

G. SARAVANAKUMAR
DEPARTMENT OF MATHEMATICS, M.KUMARASAMY COLLEGE OF ENGINEERING (AUTONOMOUS) KARUR, TAMILNADU -639 113, INDIA.
Email: saravananguru2612@gmail.com

Interval-valued Pythagorean fuzzy weak bi-hyperideals in hypersemigroups
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V.S. Subha and S. Sharmila
Annals of Communications in Mathematics, Vol. 4 (1) (2021), 35-44
Abstract

 In this paper we introduce the concept of interval-valued Pythagorean fuzzy subsemihypergroup and interval-valued Pythagorean fuzzy weak bi-hyperideals in hypersemigroups. We show that the (˜α, β˜)−level set of interval-valued Pythagorean fuzzy weak bi-hyperideal is a weak bi-hyperideal in hypersemigroup. We characterize cartesian product of interval-valued Pythagorean fuzzy set and examine that the cartesian product of interval-valued Pythagorean fuzzy weak bi-hyperideals is also an interval-valued Pythagorean weak bi-hyperideal in hypersemigroups.

V. S. SUBHA
DHARMAPURAM GNANAMBIGAI GOVT. ARTS COLLEGE(W), MAILADUTHURAI, TAMILNADU-609001, INDIA.
Email: dharshinisuresh2002@gmail.com

S. SHARMILA
ANNAMALAI UNIVERSITY, CHIDAMBARAM, TAMILNADU-608001, INDIA.
Email: gs.sharmi30@gmail.com

Regular semiopen soft sets and their applications
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E. Elavarasan and A. Vadivel
Annals of Communications in Mathematics, Vol. 4 (1) (2021), 45-62
Abstract

The purpose of this paper is to introduce the notion of soft regular semi compactness, connectedness, and separation axioms using regular semiopen soft sets in soft topological spaces. Moreover, we investigate soft RS-regular space and soft RSnormal space are soft to pological properties under bijection, soft regular semi irresolute and soft regular semi irresolute open functions. Also, we show that the properties of being soft regular semi Ti-spaces (i = 1, 2, 3, 4) are hereditary properties.

E. ELAVARASAN
DEPARTMENT OF MATHEMATICS, SHREE RAGHAVENDRA ARTS AND SCIENCE COLLEGE, KEEZHAMOONGILADI, CHIDAMBARAM-608 102, TAMIL NADU, INDIA
Email: maths.aras@gmail.com

A. VADIVEL
DEPARTMENT OF MATHEMATICS, GOVT ARTS COLLEGE (AUTONOMOUS), KARUR-639 005, TAMIL NADU, INDIA
Email: avmaths@gmail.com

On Pythagorean normal subbisemiring of bisemiring
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M. Palanikumar and K. Arulmozhi
Annals of Communications in Mathematics, Vol. 4 (1) (2021), 63-72
Abstract

We discuss the notion of Pythagorean subbisemiring, level sets of Pythagorean subbisemirings and Pythagorean normal subbisemiring of a bisemiring. Also, we investigate some of the properties related to subbisemirings. The fuzzy subset L = (πPL , ωPL ) is a Pythagorean subbisemiring if and only if all non-empty level set L(t,s) (t, s ∈ (0, 1]) is a subbisemiring. The cartesian product of two Pythagorean subbisemiring is also Pythagorean subbisemiring. The homomorphic image and preimage of Pythagorean subbisemiring is also Pythagorean subbisemiring. To illustrate our results and examples are given.

M. PALANIKUMAR
ANNAMALAI UNIVERSITY, DEPARTMENT OF MATHEMATICS, CHIDAMBARAM, 608002, INDIA
Email: palanimaths86@gmail.com

K. ARULMOZHI
ANNAMALAI UNIVERSITY, DEPARTMENT OF MATHEMATICS, CHIDAMBARAM, 608002, INDIA
Email: arulmozhiems@gmail.com

On characterization of regular ordered ternary semihypergroups by relative
hyperideals

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Abul Basar, Naveed Yaqoob, M. Y. Abbasi and Bhavanari Satyanarayana
Annals of Communications in Mathematics, Vol. 4 (1) (2021), 73-88
Abstract

In the present paper, we introduce the relative left, right, lateral, two-sided hyperideal, relative quasi-hyperideal, relative bi-hyperideal, relative sub-idempotent ordered bi-hyperideal, relative generalized quasi-hyperideal, relative generalized bi-hyperideal, relative regularity of ordered ternary semihypergroups and relative left (right, lateral) simple ordered ternary semihypergroups. We characterize relative regular ordered ternary semihypergroups through relative quasi-hyperideals and relative bi-hyperideals. We also obtain some results based on relative simple ordered ternary semihypergroups, and other results connecting these relative hyperideal-theoretic notions.

ABUL BASAR
DEPARTMENT OF NATURAL AND APPLIED SCIENCES, GLOCAL UNIVERSITY, MIRZAPUR,
SAHARANPUR, UTTAR PRADESH, 247121, INDIA
Email: basar.jmi@gmail.com

NAVEED YAQOOB
DEPARTMENT OF MATHEMATICS AND STATISTICS, RIPHAH INTERNATIONAL UNIVERSITY, I-14, ISLAMABAD, PAKISTAN
Email: naveed.yaqoob@riphah.edu.pk

MOHAMMAD YAHYA ABBASI
DEPARTMENT OF MATHEMATICS, JAMIA MILLIA ISLAMIA, NEW DELHI, 110 025, INDIA
Email: m.abbasi@gmail.com

BHAVANARI SATYANARAYANA
DEPARTMENT OF MATHEMATICS, ACHARYA NAGARJUNA UNIVERSITY, GUNTUR, ANDHRA PRADESH, 522 510, INDIA
Email: bhavanari2002@yahoo.co.in

POONAM KUMAR SHARMA
DEPARTMENT OF MATHEMATICS, D. A. V. COLLEGE, JALANDHAR, PUNJAB-144 008, INDIA
Email: pksharma@davjalandhar.com

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