The main goal of this paper is to introduce and study a new class of function via the notions of $e$-$theta$-open sets and $e$-$theta$-closure operator which are defined by Özkoç and Aslım [10] called weakly $eR$-open functions and $e$-$theta$-open functions. Moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing topolo...

Let $C_0(alpha)$ denote the class of concave univalent functions defined in the open unit disk $mathbb{D}$. Each function $f in C_{0}(alpha)$ maps the unit disk $mathbb{D}$ onto the complement of an unbounded convex set. In this paper, we study the mapping properties of this class under integral operators.

 Many efficient interior-point methods (IPMs) are based on the use of a self-concordant barrier function for the domain of the problem that has to be solved. Recently, a wide class of new barrier functions has been introduced in which the functions are not self-concordant, but despite this fact give rise to efficient IPMs. Here, we introduce the notion of locally self-concordant barrier functio...

The Schur class, denoted by $${\mathcal {S}}({\mathbb {D}})$$ , is the set of all functions analytic and bounded one in modulus open unit disc $${\mathbb {D}}$$ complex plane {C}}$$ that $$\begin{aligned} {\mathcal {D}}) = \left\{ \varphi \in H^\infty ({\mathbb {D}}): \Vert _{\infty } := \sup _{z {\mathbb {D}}} |\varphi (z)| \le 1\right\} . \end{aligned}$$ elements are called functions. A class...

In this paper, we revisit a procedure for constructing peak functions devised by Bishop. Specifically, let Ω be a bounded domain in R (or C), and let E be a closed subspace of C(Ω) : the class of all complex-valued functions that are continuous on Ω. Let x ∈ Ω; we say that f (here f ∈ E) peaks at x if f(x) = 1 and |f(y)| < 1 ∀y ∈ Ω \ {x}, and we call f a peak function of class E. We present a p...