Annals of Communications in Mathematics

For dealing with uncertainties researchers introduced the concept of soft sets. In this paper, a new class of soft sets called soft delta pre ideal open sets in soft ideal topological space related to the notion of soft pre ideal regular pre ideal open sets is introduced. Also, some new soft separation axioms based on the soft delta pre ideal open sets are investigated.

F. H. KHEDR
DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, ASSIUT UNIVERSITY, ASSIUT 71516, EGYPT.
Email: khedrf@aun.edu.eg
O. R. SAYED
DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, ASSIUT UNIVERSITY, ASSIUT 71516, EGYPT.
Email: o-sayed@aun.edu.eg
S.R. MOHAMED
DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, MINIA UNIVERSITY, MINIA, EGYPT.
Email: shaymaaragab89@mu.edu.eg

In this article, the concepts of interior, weak-interior and quasi-interior filters in a quasi-ordered Γ-semigroup are introduced and recognize some of their fundamental properties. In addition to the above, the relationships between these three classes of filters in quasi-ordered Γ-semigroups are considered. One of the specifics in this analysis, among others, is that the requirement that a filter in a quasi-ordered Γ-semigroup S has to be a sub-semigroup in S is omitted. Instead of this requirement in the determination of these three classes of filters the consistency requirement is incorporated

D. A. ROMANO
INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE, KORDUNASKA ˇ STREET 6, 78000 BANJA LUKA, BOSNIA AND HERZEGOVINA
Email: daniel.a.romano@hotmail.com

The aim of this article is to introduce fuzzy minimal e-open and fuzzy maximal e-open sets in fuzzy topological space. Further, we investigate some properties with these new sets.

M. SANKARI
DEPARTMENT OF MATHEMATICS, LEKSHMIPURAM COLLEGE OF ARTS AND SCIENCE, NEYYOOR, KANYAKUMARI, TAMIL NADU-629 802, INDIA
Email: sankarisaravanan1968@gmail.com
S.DURAI RAJ
DEPARTMENT OF MATHEMATICS, PIONNEER KUMARASWAMI COLLEGE OF ARTS AND SCIENCE, NAGERCOIL, TAMIL NADU-629 003, INDIA.
Email: durairajsprincpkc@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

This manuscript concerns the fuzzy differential equation involving ψ-Hilfer type fractional derivative with nonlocal condition. By using successive approximation, we obtain the existence, uniqueness results of solution for ψ-Hilfer fuzzy differential equation. Further, nonlocal conditions are extended to the existence results. Furthermore, an application is shown to demonstrate the theoretical conclusions utility.

K. KANAGARAJAN
DEPARTMENT OF MATHEMATICS, SRI RAMAKRISHNA MISSION VIDYALAYA COLLEGE OF ARTS AND SCIENCE, COIMBATORE-641020, INDIA.
Email: kanagarajank@gmail.com
R. VIVEK
DEPARTMENT OF MATHEMATICS, SRI RAMAKRISHNA MISSION VIDYALAYA COLLEGE OF ARTS AND SCIENCE, COIMBATORE-641020, INDIA.
Email: vivekmaths1997@gmail.com
D. VIVEK
DEPARTMENT OF MATHEMATICS, PSG COLLEGE OF ARTS AND SCIENCE, COIMBATORE-641014, INDIA.
Email: peppyvivek@gmail.com
E. M. ELSAYED
DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE,MANSOURA UNIVERSITY, MANSOURA 35516, EGYPT.
Email: emmelsayed@yahoo.com

In this article focuss on nano Ⓢ-closed sets and nano Ⓢs-closed sets are introduce and study. Also, we introduce and study nano Ⓢ-continuous functions and nano Ⓢs-continuous functions. Furthermore, we introduce the notions of nano topological spaces called nano Ⓢ-T 1/2 space and nano Ⓢ-Ts space.

I. RAJASEKARAN
DEPARTMENT OF MATHEMATICS, TIRUNELVELI DAKSHINA MARA NADAR SANGAM COLLEGE, T. KALLIKULAM627 113, TIRUNELVELI DISTRICT, TAMIL NADU, INDIA
Email: sekarmelakkal@gmail.com
N. SEKAR
DEPARTMENT OF MATHEMATICS, ARUMUGAM PILLAI SEETHAI AMMAL COLLEGE, TIRUPPATTUR, SIVAGANGAI DISTRICT, TAMIL NADU, INDIA.
Email: sekar.skrss@gmail.com
A. PANDI 
DEPARTMENT OF MATHEMATICS, RATHINAM TECHNICAL CAMPUS, COIMBATORE, TAMIL NADU, INDIA
Email: pandi2085@yahoo.com

In this paper the concept of proximity in L-fuzzifying topology is established and some of its properties are discussed. Furthermore we introduce and study the concepts ofL-fuzzifying uniform space and L-fuzzifying strong uniform space.

MOHAMMED M. KHALAF
FACULTY OF ENGINEERING, ARAB ACADEMY FOR SCIENCE & TECHNOLOGY AND MARITIME
TRANSPORT (AASTMT), ASWAN BRANCH, EGYPT
Email: khalfmohammed2003@egypt.aast.edu