Annals of Communications in Mathematics

The notion of Γ-semigroups has been introduced by M. K. Sen and N. K. Saha. The concept of (co-ordered) Γ-semigroups with apartness in Bishop’s constructive algebra was introduced by this author. Many classical notions and processes of semigroups and Γ-semigroups have been extended to (co-ordered) Γ-semigroups with apartness such as ideals, filters and the first theorem of isomorphism of this class of algebraic structures. In this paper, as a continuation of earlier research, the author designs a form of the third isomorphism theorems for Γ-semigroups and co-ordered Γ-semigroups with apartness which does not have its counterpart in the classical Γ-semigroup theory.

DANIEL A. ROMANO
INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE, 6, KORDUNASKA ˇ STREET, 78000 BANJA LUKA, BOSNIA AND HERZEGOVINA
Email: bato49@hotmail.com

 We establish the generalized Hyers-Ulam stability of the 4 variable quadratic
functional equation

in Fuzzy Normed Spaces using two different methods.

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

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

K. LOGANATHAN
DEPARTMENT OF MATHEMATICS, ERODE ARTS & SCIENCE COLLEGE, ERODE – 638 009, TAMIL NADU, INDIA.
Email: loganathankaruppusamy304@gmail.com

 In this paper, we define the notions of Pythagorean fuzzy ideal of subtraction semigroup and near subtraction semigroup. Also, we discuss some of its properties with examples.

V. CHINNADURAI
DEPARTMENT OF MATHEMATICS, ANNAMALAI UNIVERSITY, ANNAMALAINAGAR-608002, TAMILNADU, INDIA.
Email: kv.chinnadurai@yahoo.com

A. ARULSELVAM
DEPARTMENT OF MATHEMATICS, ANNAMALAI UNIVERSITY, ANNAMALAINAGAR-608002, TAMILNADU, INDIA.
Email: arulselvam.a91@gmail.com

The purpose of this paper is to introduce the concepts of fuzzy regular semi
compactness, fuzzy regular semi connectedness, fuzzy regular semi strongly connectedness and fuzzy regular semi-C5-connectedness. Some interesting properties of these notions are studied. In this connection, interrelations are discussed. Examples are provided
wherever necessary

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

In this work, we investigate the Hyers-Ulam stability by using direct and fixed point methods for the quartic functional equation

for positive integer p ≥ 3.

K. LOGANATHAN
DEPARTMENT OF MATHEMATICS, ERODE ARTS & SCIENCE COLLEGE, ERODE – 638 009, TAMIL NADU, INDIA.
Email: loganathankaruppusamy304@gmail.com

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

The purpose of this article is to study the concepts of fuzzy paraopen and fuzzy paraclosed sets in fuzzy topological spaces Further, we introduce few class of fuzzy maps namely fuzzy paracontinuous, ∗-fuzzy paracontinuous, fuzzy parairresolute, fuzzy minimal paracontinuous, fuzzy maximal paracontinuous mappings and study their prpoerties.

S. JOSEPH
RESEARCH SCHOLAR, DEPARTMENT OF MATHEMATICS, PRIST DEEMED TO BE UNIVERSITY, THANJAVUR, INDIA.
Email: jjalenjose@gmail.com

R. BALAKUMAR
DEPARTMENT OF MATHEMATICS, PRIST DEEMED TO BE UNIVERSITY, THANJAVUR, INDIA
Email: balaphdmaths@gmail.com

A. SWAMINATHAN
DEPARTMENT OF MATHEMATICS, GOVERNMENT ARTS COLLEGE(AUTONOMOUS), KUMBAKONAM, TAMIL NADU-612 002, INDIA
Email: asnathanway@gmail.com

The concepts of somewhat pairwise fuzzy e-irresolute mapping and somewhat pairwise fuzzy irresolute e-open mapping is introduced. Also some properties and comparisions of those mappings are given.

A. SWAMINATHAN
DEPARTMENT OF MATHEMATICS, GOVERNMENT ARTS COLLEGE(AUTONOMOUS), KUMBAKONAM, TAMIL NADU-612 002, INDIA
Email: asnathanway@gmail.com

M. SANKARI
DEPARTMENT OF MATHEMATICS, LEKSHMIPURAM COLLEGE OF ARTS AND SCIENCE, NEYYOOR, KANYAKUMARI, TAMIL NADU-629 802, INDIA.
Email: sankarisaravanan1968@gmail.com

 In this paper, we introduce the notion of anti N -H-ideals of a BCK-algebra. Then, the notion of the direct product of two anti N -H-ideals by using minimum operation is introduced, and some related properties are studied. Ordinary H-ideals are linked with anti N -H-ideals by means of an anti N -s-level set of the direct product of two N – structures.

ANAS AL-MASARWAH
SCHOOL OF MATHEMATICAL SCIENCES, FACULTY OF SCIENCE AND TECHNOLOGY, UNIVERSITI KEBANGSAAN MALAYSIA, 43600 UKM BANGI, SELANGOR DE, MALAYSIA.
Email: almasarwah85@gmail.com

The object of the present paper is to characterize e − LP −Sasakian manifolds with a quarter-symmetric metric connection admitting η−Ricci solitons. Finally, the existence of η−Ricci soliton in an e − LP −Sasakian manifold has been proved by a concrete example.

ABDUL HASEEB
DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, JAZAN UNIVERSITY, JAZAN, KINGDOM OF SAUDI ARABIA
Email: malikhaseeb80@gmail.com, haseeb@jazanu.edu.sa

LOVEJOY S. DAS
DEPARTMENT OF MATHEMATICS, KENT STATE UNIVERSITY, KENT, USA.
Email: ldas@kent.edu

MOBIN AHMAD
DEPARTMENT OF MATHEMATICS, INTEGRAL UNIVERSITY, LUCKNOW, INDIA.
Email: mobinahmad@rediffmail.com

 In this paper, we introduce the notions of interval rough fuzzy Γ-ideals, bi-Γideal, prime-Γ- ideal and prime-bi-Γ-ideal in Γ-semigroup and establish some interesting properties of these structures.

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

P. DHANALAKSHMI 
ANNAMALAI UNIVERSITY, ANNAMALAI NAGAR-608002
Email: vpdhanam83@gmail.com