-convex sets and -convex functions, which are considered as an important class of generalized convex sets and convex functions, have been introduced and studied by Youness [5] and other researchers. This class has recently extended, by Youness, to strongly -convex sets and strongly -convex functions. In these generalized classes, the definitions of the classical convex sets and convex functions are relaxed and introduced with respect to a mapping . In this paper, new properties of strongly -convex sets are presented. We define strongly -convex hull, strongly -convex cone, and strongly -convex cone hull and we proof some of their properties.  Some examples to illustrate the aforementioned concepts and to cl

In this paper, we will focus to one of the recent applications of PU-algebras in the coding theory, namely the construction of codes by soft sets PU-valued functions. First, we shall introduce the notion of soft sets PU-valued functions on PU-algebra and investigate some of its related properties.Moreover, the codes generated by a soft sets PU-valued function are constructed and several examples are given. Furthermore, example with graphs of binary block code constructed from a soft sets PU-valued function is constructed.

Contents IJPAM: Volume 116, No. 3 (2017)

  In this paper, the concept of normalized duality mapping has introduced in real convex modular spaces. Then, some of its properties have shown which allow dealing with results related to the concept of uniformly smooth convex real modular spaces. For multivalued mappings defined on these spaces, the convergence of a two-step type iterative sequence to a fixed point is proved

This paper work new and unprecedented definitions of sets, which we have named supra fan, supra. delta fan, supra. semi delta fan sets, which are generated by three sets of specific type of supra open sets, it was utilized supra open, supra delta open, supra. semi delta open sets with special conditions. It is highlighted many details of these new types of fan sets, their axis, blades and their annular sets using tables. Attention is given to the interior and the closure of these three types in supra topological spaces. The research was further enriched numerous and diverse examples. Subsequently, the focus shifted to supra. semi delta fan sets to prove lemma and theorem.

In this thesis, we introduced some types of fibrewise topological spaces by using a near soft set, various related results also some fibrewise near separation axiom concepts and a fibrewise soft ideal topological spaces. We introduced preliminary concepts of topological spaces, fibrewise topology, soft set theory and soft ideal theory. We explain and discuss new notion of fibrewise topological spaces, namely fibrewise soft near topological spaces, Also, we show the notions of fibrewise soft near closed topological spaces, fibrewise soft near open topological spaces, fibrewise soft near compact spaces and fibrewise locally soft near compact spaces. On the other hand, we studied fibrewise soft near forms of the more essent