Upper and Lower $(I,J)$-Continuous Multifunctions

NOVI SAD JOURNALS OF MATHEMATICS, 2019

The purpose of the present paper is to introduce, study and characterize the upper and lower almost contra (I; J)-continuous multi- functions. Also, we investigate their relation with another well known class of continuous multifunctions.

2019

The purpose of the present paper is to introduce, study and characterize upper and lower weakly (I, J)-continuous multifunctions and contra (I, J)-continuous multifunctions. Also, we investigate its relation with another class of continuous multifunctions.

2021

Given a multifunction F : (X; _ ) ! (Y; _), _; _ oper-ators on (X; _ ), _; _ operators on (Y; _) and I a proper ideal on X. The purpose of the present paper is to introduce, study and characterize upper and lower (_; _; _; _; I)-continuous multifunctions, its relation with another class of continuous multifunctions. Also, we introduce a general decomposition form for this class of continuous multifunction

Matematychni Studii. , 2021

Let (X;  ) and (Y; ) be topological spaces in which no separation axioms are assumed, unless explicitly stated and if I is an ideal on X. Given a multifunction F : (X;  ) ! (Y; ), ; operators on (X;  ), ;  operators on (Y; ) and I a proper ideal on X. We introduce and study upper and lower ( ; ; ; ; I)-continuous multifunctions. A multifunction F : (X;  ) ! (Y; ) is said to be: 1) upper-( ; ; ; ; I)-continuous if (F+((V ))) n (F+((V ))) 2 I for each open subset V of Y ; 2) lower-( ; ; ; ; I)-continuous if (F􀀀((V ))) n (F􀀀((V ))) 2 I for each open subset V of Y ; 3) ( ; ; ; ; I)-continuous if it is upper- and lower-( ; ; ; ; I)- continuous. In particular, the following statements are proved in the article (Theorem 2): Let ; be operators on (X;  ) and ; ;  operators on (Y; ): 1. The multifunction F : (X;  ) ! (Y; ) is upper ( ; ;  \ ; ; I)-continuous if and only if it is both upper ( ; ; ; ; I)-continuous and upper ( ; ; ; ; I)-continuous. 2. The multifunction F : (X;  ) ! (Y; ) is lower ( ; ;  \ ; ; I)-continuous if and only if it is both lower ( ; ; ; ; I)-continuous and lower ( ; ; ; ; I)-continuous, provided that (A \ B) = (A) \ (B) for any subset A;B of X.

International Journal of Mathematical Analysis

The aim of this paper is to introduce and study upper and lower almost γ-M continuous multifunctions from an m-space into a topological space.

Lobachevskii Journal of Mathematics, 2009

In this paper, we introduce and study the notion of almost contra-continuous multifunctions. Characterizations and properties of almost contra-continuous multifunctions are discussed.

Matematychni Studii, 2021

Let $(X, \tau)$ and $(Y, \sigma)$ be topological spaces in which no separation axioms are assumed, unless explicitly stated and if $\mathcal{I}$ is an ideal on $X$.Given a multifunction $F\colon (X, \tau)\rightarrow (Y, \sigma)$, $\alpha,\beta$ operators on $(X, \tau)$, $\theta,\delta$ operators on $(Y, \sigma)$ and $\mathcal{I}$ a proper ideal on $X$. We introduce and study upper and lower $(\alpha, \beta,\theta,\delta,\mathcal{I})$-continuous multifunctions.A multifunction $F\colon (X, \tau)\rightarrow (Y, \sigma)$ is said to be: {1)} upper-$(\alpha, \beta,\theta,\delta,\mathcal{I})$-continuous if $\alpha(F^{+}(\delta(V)))\setminus \beta(F^{+}(\theta(V)))\in \mathcal{I}$ for each open subset $V$ of $Y$;\{2)} lower-$(\alpha, \beta,\theta,\delta,\mathcal{I})$-continuous if$\alpha(F^{-}(\delta(V)))\setminus \beta(F^{-}(\theta(V)))\in \mathcal{I}$ for each open subset $V$ of $Y$;\ {3)} $(\alpha, \beta,\theta,\delta,\mathcal{I})$-continuous if it is upper-\ %$(\alpha, \beta,\theta,\del...

viXra, 2020

In this paper, we introduce and study upper and lower slightly $\delta$-$\beta$- continuous multifunctions in topological spaces and obtain some characterizations of these new continuous multifunctions.

Real Analysis Exchange

The aim of this paper is to improve some recent results of Noiri and Popa on multifunctions by utilizing the concepts of almost β-continuous and weakly α-continuous multifunctions. We give some more results on strong irresolvability.

2014

The purpose of this paper is to introduce and study a new generalization of ω-continuous multifunction called slightly ω-continuous multifunctions in topological spaces. AMS (MOS) Subject Classification Codes: 54C10, 54C08, 54C05