Approximation of continuous and quasi-continuous functions by monotone functions

Contra $beta^{*}$-continuous and almost contra $beta^{*}$-continuous functions

The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion of $beta^{*}$-closed sets in topological space to present and study a new class of functions called contra $beta^{*}$-continuous and almost contra $beta^{*}$-continuous functions as a new generalization of contra continuity.

Generalized Rings of Measurable and Continuous Functions

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

Averages of Quasi-continuous Functions

The goal of this paper is to characterize the family of averages of comparable (Darboux) quasi-continuous functions.

Of Approximation by Polynomials to Continuous Functions

Fitzpatrick Functions and Continuous Linear Monotone Operators

The notion of a maximal monotone operator is crucial in optimization as it captures both the subdifferential operator of a convex, lower semicontinuous, and proper function and any (not necessarily symmetric) continuous linear positive operator. It was recently discovered that most fundamental results on maximal monotone operators allow simpler proofs utilizing Fitzpatrick functions. In this pa...