Annals of Communications in Mathematics

The concept of statistical summability C, 1)(H, 1) has recently been introduced by [8]. In this paper we establish some inequalities related to concept of statistical summability (C, 1)(H, 1).

M. MURSALEEN
DEPARTMENT OF MATHEMATICS, ALIGARH MUSLIM UNIVERSITY, ALIGARH, 202002, INDIA
Email: mursaleenm@gmail.com

This paper is concerned with the existence of two nontrivial positive solutions to a class of boundary value problems involving a p-Laplacian of the form

where Φp(x) = |x|
p−2x is a one dimensional p-Laplacian operator with p > 1, a and b are real constants, and α and β are given by the Riemann-Stieltjes integrals

with A and B functions of bounded variation. The approach used is based on fixed point index theory. The results obtained in this paper are new in the literature.

SESHADEV PADHI
DEPARTMENT OF MATHEMATICS, BIRLA INSTITUTE OF TECHNOLOGY, MESRA, RANCHI – 835215, INDIA
Email: spadhi@bitmesra.ac.in

JAFFAR ALI
DEPARTMENT OF MATHEMATICS, FLORIDA GULF COAST UNIVERSITY, FORTMYRES, FLORIDA 33965, USA
Email: jashaulhameed@fgcu.edu

JOHN R. GRAEF
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF TENNESSEE AT CHATTANOOGA, CHATTANOOGA, TN 37403, USA
Email: john-graef@utc.edu

In this paper, we establish the concept of hesitant intuitionistic fuzzy soft ideals and hesitant intuitionistic fuzzy soft b-ideals are introduced and investigated. Also, the power-m, and ρ-multiply are defined in the hesitant intuitionistic fuzzy soft set theory to BCK-algebras. Finally, the newly introduced notions of the complement of a hesitant intuitionistic soft set (ideals and b-ideals) are discussed.

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

M. BALAMURUGAN
DEPARTMENT OF MATHEMATICS, SRI VIDYA MANDIR ARTS AND SCIENCE COLLEGE, UTHANGARAI, TAMIL NADU-636902, INDIA
Email: balamurugansvm@gmail.com

 Fuzzy multigroup is a structure that generalizes the idea of fuzzy group. In fact, the concept of fuzzy multigroups is the application of fuzzy multisets to group theory. The idea of direct product of fuzzy multigroups has been established. This paper extends the notion of direct product between two fuzzy multigroups to the case of finitely many fuzzy multigroups. Some properties of generalized direct product of fuzzy multigroups are elucidated. It is shown that generalized direct product of fuzzy multigroups is a fuzzy multigroup. Finally, a number of results are obtained and duly verified with respect to alph-cuts and level sets.

P. A. EJEGWA
DEPARTMENT OF MATHEMATICS/STATISTICS/COMPUTER SCIENCE, UNIVERSITY OF AGRICULTURE, P.M.B. 2373, MAKURDI, NIGERIA
Email: ejegwa.augustine@uam.edu.ng;  ocholohi@gmail.com

 In this manuscript, our concern is to introduce the new approach of studying the lacunary almost statistical convergence and strongly almost convergence of the generalized difference sequences of fuzzy numbers. Some interesting and basic properties concerning them will be studied.

ABDUL HAMID GANIE
COLLEGE OF SCIENCES AND THEORETICAL STUDIES,, SAUDI ELECTRONIC UNIVERSITY-SAUDI ARABIA
Email: a.ganie@seu.edu.sa

 The notions of doubt N -subalgebras and doubt N -ideals in BCK-algebras are introduced, and related properties are investigated. Characterizations of a doubt N – subalgebra and a doubt N -ideal are given, and relations between them are discussed.

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

ABD GHAFUR AHMAD
SCHOOL OF MATHEMATICAL SCIENCES, FACULTY OF SCIENCE AND TECHNOLOGY, UNIVERSITI KEBANGSAAN MALAYSIA, 43600 UKM BANGI, SELANGOR DE, MALAYSIA
Email: ghafur@ukm.edu.my

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

The aim of the present paper is to define and bring together the fundamental definitions such as relative hyperideals, relative bi-hyperideals, relative quasi-hyperideals, relative prime hyperideals, relative weakly prime hyperideals, relative semiprime hyperideals, relative prime and relative semiprime bi-hyperideals, and hyper relative regularity of dynamic algebraic character to develop the theory of hypersemigroups, and obtain the results relating to and connecting these hyperideal-theoretic definitions of this vast theory to the larger framework of the algebraic area of ordered hypersemigroups as well as of involution ordered hypersemigroups.

ABUL BASAR
DEPARTMENT OF NATURAL AND APPLIED SCIENCES, GLOCAL UNIVERSITY, MIRZAPUR, SAHARANPUR, UTTAR PRADESH–247 121, INDIA
Email: basar.jmi@gmail.com

 In this work, authors investigate the generalized Hyers-Ulam stability of the 4-variable quadratic functional equation of the form

in Banach spaces.

K. TAMILVANAN
DEPARTMENT OF MATHEMATICS, GOVERNMENT ARTS COLLEGE(MEN), KRISHNAGIRI-635 001, TAMILNADU, INDIA.
Email: tamiltamilk7@gmail.com

K. LOGANATHAN
DEPARTMENT OF MATHEMATICS, FACULTY OF ENGINEERING, KARPAGAM ACADEMY OF HIGHER EDUCATION, COIMBATORE-641 021, TAMILNADU, INDIA.
Email: loganathankaruppusamy304@gmail.com

K. MOHANA
DEPARTMENT OF MATHEMATICS, SASURI COLLEGE OF ENGINEERING, TIRUPUR-638 056, TAMILNADU , INDIA.
Email: monathen14@gmail.com

The paper introduces the notions of bipolar fuzzy BCI-implicative ideals and bipolar fuzzy closed BCI-implicative ideals of BCI-algebras. It is proved that any bipolar fuzzy BCI-implicative ideal is a bipolar fuzzy ideal but not the converse. Characterizations of bipolar fuzzy BCI-implicative ideals and bipolar fuzzy closed BCIimplicative ideals are given and more properties are studied.

D. AL-KADI
TAIF UNIVERSITY, DEPARTMENT OF MATHEMATICS AND STATISTIC, TAIF, 21974, SAUDI ARABIA
Email: dak12le@hotmail.co.uk

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

In this paper, we study some properties of hesitant fuzzy ideals and hesitant fuzzy bi-ideals in a semigroup and discuss their characterizations. Also we introduce hesitant fuzzy interior ideals in a semigroup and studied their properties. It is proved that in a semigroup a hesitant fuzzy ideal is a hesitant fuzzy interior ideal but the converse is not true. Moreover we prove that in regular and in intra-regular semigroups the hesitant fuzzy ideals and the hesitant fuzzy interior ideals coincide.

AAKIF FAIROOZE TALEE
DEPARTMENT OF SCHOOL EDUCATION, KASHMIR-192124, INDIA
Email: fuzzyaakif786.jmi@gmial.com

M. Y. ABBASI
DEPARTMENT OF MATHEMATICS, JAMIA MILLIA ISLAMIA, NEW DELHI-110025, INDIA
Email: mabbasi@jmi.ac.in

A. BASAR
DEPARTMENT OF MATHEMATICS, JAMIA MILLIA ISLAMIA, NEW DELHI-110025, INDIA
Email: basar.jmi@gmail.com

We examine the Ulam-Hyers stability of finite variable additive functional equation in fuzzy normed space using classical methods.

K. TAMILVANAN
DEPARTMENT OF MATHEMATICS, GOVERNMENT ARTS COLLEGE(MEN), KRISHNAGIRI-635 001, TAMILNADU, INDIA.
Email: tamiltamilk7@gmail.com

K. LOGANATHAN
DEPARTMENT OF MATHEMATICS, FACULTY OF ENGINEERING, KARPAGAM ACADEMY OF HIGHER EDUCATION, COIMBATORE-641 021, TAMILNADU, INDIA
Email: loganathankaruppusamy304@gmail.com