Annals of Communications in Mathematics

 Employing sequential generalized Caputo fractional left and right vectorial Taylor formulae we establish mixed sequential generalized fractional Ostrowski and Gruss ¨ type inequalities for several Banach algebra valued functions. The estimates are with respect to all norms k·kp , 1 ≤ p ≤ ∞. We finish with applications.

GEORGE A. ANASTASSIOU
DEPARTMENT OF MATHEMATICAL SCIENCES, UNIVERSITY OF MEMPHIS, MEMPHIS, TN 38152, U.S.A.
Email: ganastss@memphis.edu

We study the existence and uniqueness of positive solutions of the nonlinear
fractional relaxation differential equation

where Dα/1 is the Caputo-Hadamard fractional derivative of order 0 < α ≤ 1. In the process we convert the given fractional differential equation into an equivalent integral equation. Then we construct an appropriate mapping and employ the Schauder fixed point theorem and the method of upper and lower solutions to show the existence of a positive solution of this equation. We also use the Banach fixed point theorem to show the existence of a unique positive solution. Finally, 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
AHCENE DJOUDI
APPLIED MATHEMATICS LAB., FACULTY OF SCIENCES, DEPARTMENT OF MATHEMATICS, UNIVERSITY OF ANNABA, P.O. BOX 12, ANNABA, 23000, ALGERIA
Email: adjoudi@yahoo.com

From the nature of subbisemiring, we develop a new generalized hybrid structure of vague subbisemiring known as cubic vague subbisemiring (shortly CVSBS). We talk about the CVSBS and level sets CVSBS of bisemiring. At first we define some basic operation such as intersection, cartesian product on them and use these to obtain some of its basic properties under CVSBS. Let L = hA¯L, VLi be the cubic vague subset of S. It is shown that L is a CVSBS if and only if all non empty level set L(α,β) (α, β ∈ D[0, 1]) is a SBS. Let L be the CVSBS and W be the strongest vague relation of S. We show that L is a CVSBS if and only if W is a CVSBS of S × S. After we define homomorphic image and preimage of bisemiring. It will be shown that the homomorphic image and preimage
of CVSBS is a CVSBS. To strengthen our results with examples are indicated.

M. PALANIKUMAR
ANNAMALAI UNIVERSITY, DEPARTMENT OF MATHEMATICS, CHIDAMBARAM, 608002, INDIA.
Email: palanimaths86@gmail.com
K. ARULMOZHI
BHARATH INSTITUTE OF HIGHER EDUCATION AND RESEARCH, DEPARTMENT OF MATHEMATICS, CHENNAI, 600073, INDIA
Email: arulmozhiems@gmail.com

The aim of this paper is to introduce and study the concept of somewhat fuzzy completely e-irresolute mapping and somewhat fuzzy irresolute e-open mapping. Further, some interesting properties of those mappings are given and some comparative results discussed.

M. SANKARI
DEPARTMENT OF MATHEMATICS, LEKSHMIPURAM COLLEGE OF ARTS AND SCIENCE, NEYYOOR, KANYAKUMARI, TAMIL NADU-629 802, INDIA.
Email: sankarisaravanan1968@gmail.com
C. MURUGESAN
RESEARCH SCHOLAR, PIONNEER KUMARASWAMI COLLEGE OF ARTS AND SCIENCE,VETTURINIMADAM, KANYAKUMARI, TAMIL NADU-629 003, INDIA.(AFFILIATED TO MANONMANIAM SUNDARANAR UNIVERSITY, TIRUNELVELLI)
Email: kumarithozhanmurugesan@gmail.com

In this paper, we introduce and study the concept of regular semi continuous, regular semi irresolute, regular semi-T1/2 space, regular semi homeomorphisms and regular semi c-homeomorphisms in neutrosophic topological spaces. Moreover, we investigate the relationship among neutrosophic regular semi continuous, neutrosophic regular semi irresolute, neutrosophic regular semi homeomorphism and neutrosophic regular semi Chomeomorphisms mappings. Finally, we have given some counter examples to show that these types of mappings are not equivalent.

R. VIJAYALAKSHMI
DEPARTMENT OF MATHEMATICS, ARIGNAR ANNA GOVERNMENT ARTS COLLEGE, NAMMAKKAL, TAMIL NADU-637 002, INDIA
Email: vijilakshmi80@redif fmail.com
R. R. PRAVEENA
RESEARCH SCHOLAR, DEPARTMENT OF MATHEMATICS, ANNAMALAI UNIVERSITY, ANNAMALAINAGAR, TAMIL NADU-608 002, INDIA.
Email: praveenaphd24@gmail.com

In the present communication, we introduce the theory of generalized spherical fuzzy soft set and define some operations such as complement, union, intersection, AND and OR. Notably, we tend to showed De Morgan’s laws, associate laws and distributive laws that are holds in generalized spherical fuzzy soft set. Also, we advocate
an algorithm to solve the decision making problem based on generalized soft set model. We introduce a similarity measure of two generalized spherical fuzzy soft sets and discuss its application in a medical diagnosis problem. Suppose that there are five patients P₁, P₂, P₃, P₄ and P₅ in a hospital with certain symptoms of dengue hemorrhagic fever. Let the universal set contain only three elements. That is X = {x1 : severe, x2: mild,
x3 : no}, the set of parameters E is the set of certain symptoms of dengue hemorrhagic fever is represented by E = {e1 : severe abdominal pain, e2: persistent vomiting, e3 : rapid breathing, e4 : bleeding gums, e5: restlessness and blood in vomit}. An illustrative examples are mentioned to show that they can be successfully used to solve problems with uncertainties.

M. PALANIKUMAR
ANNAMALAI UNIVERSITY, DEPARTMENT OF MATHEMATICS, CHIDAMBARAM, 608002, INDIA.
Email: palanimaths86@gmail.com
K. ARULMOZHI
BHARATH INSTITUTE OF HIGHER EDUCATION AND RESEARCH, DEPARTMENT OF MATHEMATICS, CHENNAI, 600073, INDIA
Email: arulmozhiems@gmail.com

The algebraic system Γ-near rings was introduced by Satyanarayana. Tamizh and Ganesan introduced the concept of bi-ideals in near-rings [On bi-ideals of near-rings, Indian J. Pure Appl. Math., 18(11), 1002-1005(1987)]. Tamizh and Meenakumari defined the concept of bi-ideals in Γ-near-rings and characterized Γ-near-fields [Bi-Ideals of Gamma Near-Rings, Southeast Asian Bulletin of Mathematics(2004), 27: 983-988].
Satyanarayana, Yahya, Basar and Kuncham studied abstract affine Γ-nearrings [Some Results on Abstract Affine Gamma-Near-Rings, International Journal of Pure and Applied Mathematical Sciences, 7(1) (2014), 43-49]. Recently, Basar, Satyanarayana, Kuncham, Kumar and Yahya studied some relative ideals in Γ-nearrings [A note on relative Γ-ideals in abstract affine Γ-nearrings, GIS Science Journal, 8(10)(2021), 9-13]. In this paper, we study relative quasi-Γ-ideals and relative bi-Γ-ideals in Γ-near rings. We also proved nice characterizations of Γ-near rings by these basic relative Γ-ideals.

ABUL BASAR
DEPARTMENT OF NATURAL AND APPLIED SCIENCES, GLOCAL UNIVERSITY, MIRZAPUR,
SAHARANPUR, U. P., INDIA.
Email: basar.jmi@gmail.com
MOHAMMAD YAHYA ABBASI
DEPARTMENT OF MATHEMATICS, JAMIA MILLIA ISLAMIA, NEW DELHI, INDIA.
Email: mabbasi@jmi.ac.in
BHAVANARI SATYANARAYANA
DEPARTMENT OF MATHEMATICS, ACHARYA NAGARJUNA UNIVERSITY, A. P., INDIA.
Email: bhavanari2002@yahoo.co.in
AAKIF FAIROOZE TALEE
DEPARTMENT OF SCHOOL EDUCATION, KASHMIR, INDIA
Email: fuzzyaakif786.jmi@gmial.com

The concept of multisets emerged by violating a principle of distinct collection of object in crisp sets. In some practical situations, multisets with multiplicity of their objects varying overtime are frequently encountered, such multisets are called dynamic multisets. However, there has been no formal mathematical study on dynamic multisets. Dynamic multiset is a special kind of multiset with time varying multiplicity of elements. The importance of dynamic multisets stems from their potential usefulness in resolving a task of finding duplicate records within large databases. In this paper, we vividly explore the concept of dynamic multisets and present some of its properties. We observe that, the operations on dynamic multisets are the same as that of static multisets, with the time parameter as the only distinction. Finally, some application-driven examples of dynamic multisets are presented.

T. O. WILLIAM-WEST
DEPARTMENT OF MATHEMATICS, AHMADU BELLO UNIVERSITY, ZARIA, NIGERIA.
Email: westtamuno@gmail.com
P. A. EJEGWA
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF AGRICULTURE, P.M.B. 2373, MAKURDI, NIGERIA
Email: ejegwa.augustine@uam.edu.ng
A. U. AMAONYEIRO
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF AGRICULTURE, P.M.B. 2373, MAKURDI, NIGERIA.
Email: ucheanslem@gmail.com

In this paper, we introduce the concept of ordered quasi-hyperideals of regular ordered semihypergroups, and study the basic results on ordered quasi-hyperideals of ordered semihypergroups. We also investigate regular ordered semihypergroups in terms of its ordered quasi-hyperideals, ordered right hyperideals and ordered left hyperideals. We prove that: (i) A partially ordered semihypergroup S is regular if and only if for every ordered bi-hyperideal B, every ordered hyperideal I and every ordered quasi-hyperideal Q, we have B ∩ I ∩ Q ⊆ (B ◦ I ◦ Q], and (ii) A partially ordered semihypergroup S is regular if and only if for every ordered quasi-hyperideal Q, every ordered left hyperideal L and every ordered right-hyperideal R, we have R ∩ Q ∩ L ⊆ (R ◦ Q ◦ L].

ABUL BASAR
DEPARTMENT OF NATURAL AND APPLIED SCIENCES, GLOCAL UNIVERSITY, MIRZAPUR, SAHARANPUR, U. P., INDIA.
Email: basar.jmi@gmail.com
MOHAMMAD YAHYA ABBASI
DEPARTMENT OF MATHEMATICS, JAMIA MILLIA ISLAMIA, NEW DELHI, INDIA.
Email: mabbasi@jmi.ac.in

In this paper, by combinig the notions of m-polar fuzzy structures and interval valued m-polar fuzzy structures, the notion of m-polar cubic structures is introduced and applied on the ideal theory of BCK/BCI-algebras. In this respect, the notions of m-polar cubic subalgebras and m-polar cubic (commutative) ideals are introduced and some essential properties are discussed. Characterizations of m-polar cubic subalgebras and m-polar cubic (commutative) ideals are considered. Moreover, the relations among m-polar cubic subalgebras, m-polar cubic ideals and m-polar cubic commutative ideals are obtained.

G. MUHIUDDIN
DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, UNIVERSITY OF TABUK, P.O. BOX 741, TABUK 71491, SAUDI ARABIA
Email: chishtygm@gmail.com
AHSAN MAHBOOB
DEPARTMENT OF MATHEMATICS, MADANAPALLE INSTITUTE OF TECHNOLOGY & SCIENCE, MADANAPALLE517325, INDIA
Email: khanahsan56@gmail.com