Annals of Communications in Mathematics

We present here generalized Canavati type g-fractional Iyengar and Ostrowski type inequalities. Our inequalities are with respect to all Lp norms: 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

The notion of (α, e βe)-fuzzy left (right, lateral) ideal is introduced, and related properties are investigated. Also, characterizations of an (∈, ∈ ∨ q δ 0 )-fuzzy left (resp., right, lateral) ideal are provided. Moreover, relations between (∈, ∈ ∨ q δ 0 )-fuzzy left (resp., right, lateral) ideal and (q δ 0 , ∈ ∨q δ 0 )-fuzzy left (resp., right, lateral) ideal are established.

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

NOOR REHMAN
DEPARTMENT OF MATHEMATICS & STATISTICS,, RIPHAH INTERNATIONAL UNIVERSITY, HAJJ COMPLEX I-14 ISLAMABAD 44000, PAKISTAN
Email: noorrehman82@yahoo.com

YOUNG BAE JUN
DEPARTMENT OF MATHEMATICS EDUCATION, GYEONGSANG NATIONAL UNIVERSITY, JINJU 660-701, KOREA
Email: skywine@gmail.com

In this paper, we introduce Hermite-Chebyshev polynomials of two variables and to give some properties of Hermite and Chebyshev polynomials of two variables. We derive series representation, operational identities, generating functions and power series method by Hermite, Chebyshev and Hermite-Chebyshev polynomials of two variables. Finally, we consider generalized Hermite-Chebyshev polynomials of two variables and explicit representation of Hermite-Chebyshev polynomials of two variables.

WASEEM A. KHAN
DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, INTEGRAL UNIVERSITY, LUCKNOW-226026,, INDIA
Email: waseem08 khan@rediffmail.com

 In this paper, the notions of (∈, ∈ ∨(k ∗, qk))-fuzzy left Γ-ideals, (∈, ∈ ∨(k ∗, qk))-fuzzy right Γ-ideals and (∈, ∈ ∨(k ∗, qk))-fuzzy Γ-ideals in ordered Γ-semigroups are introduced and their related properties are investigated. Furthermore, (k ∗, k)-lower parts of (∈, ∈ ∨(k ∗, qk))-fuzzy left Γ-ideals, (∈, ∈ ∨(k ∗, qk))-fuzzy right Γ-ideals and (∈, ∈ ∨(k ∗, qk))-fuzzy Γ-ideals are also defined. Finally, left regular, right regular and regular ordered Γ-semigroups in terms of (∈, ∈ ∨(k ∗, qk))-fuzzy left Γ-ideals and (∈, ∈ ∨(k ∗, qk))-fuzzy right Γ-ideals are characterized.

AHSAN MAHBOOB
DEPARTMENT OF MATHEMATICS, ALIGARH MUSLIM UNIVERSITY, ALIGARH-202002, INDIA.
Email: khanahsan56@gmail.com

NOOR MOHAMMAD KHAN
DEPARTMENT OF MATHEMATICS, ALIGARH MUSLIM UNIVERSITY, ALIGARH-202002, INDIA
Email: nm khan123@yahoo.co.in

This paper is an attempt to summarize the basic concepts of the theories of multiset and fuzzy multiset. We begin by describing multisets and the operations between them with some related results. In the same vein, the basic concepts of fuzzy multiset theory as well as the operations between fuzzy multisets are buttressed in relation to multiset theory. Finally, we present some properties of fuzzy multisets with some related results.

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

 This manuscript is devoted to study a new concept of intuitionistic bipolar neutrosophic set with the operations like union, intersection and complement. Also, an application to intuitionistic bipolar neutrosophic graph with examples are developed. Further, we presented the Cartesian product, cross product, lexicographic product and strong product with suitable examples

S. SATHAM HUSSAIN
PG AND RESEARCH DEPARTMENT OF MATHEMATICS, JAMAL MOHAMED COLLEGE, TRICHY – 620 020, TAMIL NADU, INDIA.
Email: sathamhussain5592@gmail.com

SAID BROUMI
LABORATORY OF INFORMATION PROCESSING, FACULTY OF SCIENCE BEN MSIK, UNIVERSITY HASSAN II, B.P 7955, SIDI OTHMAN, CASABLANCA, MOROCCO.
Email: broumisaid78@gmail.com

YOUNG BAE JUN
DEPARTMENT OF MATHEMATICS EDUCATION, GYEONGSANG NATIONAL UNIVERSITY, JINJU 52828, KOREA
Email: skywine@gmail.com

DURGA NAGARAJAN
DEPARTMENT OF MATHEMATICS, THE GANDHIGRAM RURAL INSTITUTE (DEEMED TO BE UNIVERSITY), GANDHIGRAM – 624 302, TAMIL NADU, INDIA.
Email: durga1992mdu@gmail.com