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Quite recently, a new minimal structure m^\star_H has been introduced in [ ] by using a minimal structure m and a hereditary class H. In this paper, we introduce and investigate the notion of H-scattedness in a hereditary minimal space (X, m, H).

abstract: An m-structure is introduced and investigated in [7]. A hereditary class H is defined and investigated in [1]. In this paper, we introduce and investigate generalizations of regularity and normality in a hereditary m-space (X; m;H).

In this paper, we investigate some properties \ of $\theta_{g}$-continuous and weakly $g$-continuous functions in a topological spaces. Moreover, the relationships with other related functions are investigated.

In this paper, an attempt is being made to discuss a class of modified Bessel- type integrals on a set of generalized functions known as Boehmians. We show that the modified Bessel-type integral, with appropriately defined convolution products, obeys a fundamental convolution theorem which consequently justifis pursuing analysis in the Boehmian spaces. We describe two Fréchet spaces of Boehmians and extend the modifid Bessel-type integral between the diferent spaces. Furthermore, a convolution theorem and a class of basic properties of the extended integral such as linearity, continuity and compatibility with the classical integral, which provide a convenient extention to the classical results, have been derived

The purpose of the present paper is to introduce and investigate two new classes of continuous multifunctions called upper/lower $e$-$\I$-continuous multifunctions and upper/lower $\delta\beta_I$-continuous multifunctions by using the concepts of $e$-$\I$-open sets and $\delta\beta_I$-open sets. The class of upper/lower $e$-$\I$-continuous multifunctions is contained in that of upper/lower $\delta\beta_I$-continuous multifunctions. Several characterizations and fundamental properties concerning upper/lower $e$-$\I$-continuity and upper/lower $\delta\beta_I$-continuity are obtained.

In this paper, we introduce and investigate a new class of sets called A -open sets which are weaker than co-zero sets. Moreover, we obtain characterizations and preserving theorems of quasi compact spaces.

This paper investigates some variant of Whittaker integral operators on a class of square integrable Boehmians. We define convolution products and derive the convolution theorem which substantially satisfy the axioms necessary for generating the Whittaker spaces of Boehmians. Relied on this analysis, we give a definition and properties of the Whittaker integral operator in the class of square integrable Boehmians. The extended Whittaker integral operator, is well-defined, linear and coincides with the classical integral in certain properties.

In this paper, we introduce and investigate the notions of weakly G-semi-open sets and weakly G-preopen sets in grill topological spaces. Furthermore, by using these sets we obtain new decompositions of continuity.

An ideal on a set X is a nonempty collection of subsets of X withheredity property which is also closed finite unions. The concept of ideal m-spaces was introduced by Al-Omari and Noiri [1]. In this paper, we introduce and study an operator Psi_{*} : P(X) rightarrow M defined as follows for every A in X, Psi_{*}(A) = {x in X :there exists a U in M(x) such that U − A in I}, and observes that Psi_{*}(A) =X − (X − A)_{*}.

We introduce the notions of locally b-closed, b-t-set, b-B-set, locally b-closed continuous, b-t-continuous, b-B-continuous functions and obtain decomposition of continuity and complete continuity.

see paper "On Psi ∗-operator in ideal m-spaces" v. 30 1(2012): 53-66.