Newton and quasi-Newton methods have been used in chemical process design and optimization calculations for quite some time. They continue to be used today, both in the traditional sense and as part of the more recent hybrid method. While Newton-based fixed-point methods have been used to solve many different kinds of chemical process design and optimization problems, perhaps the point of singl...

In 2009, Ilić and Rakoc̆ević proved that quasi-contraction maps on normal cone metric spaces have a unique fixed point (Ilić and Rakoc̆ević, 2009 [6]). Then, Kadelburg, Radenović and Rakoc̆ević generalized their results by considering an additional assumption (Kadelburg et al., 2009 [7]). Also, they proved that quasi-contraction maps on cone metric spaces have the property (P) whenever λ ∈ (0, 2 )...

Descriptive set theory was originally developed on Polish spaces. It was later extended to $\omega$-continuous domains [Selivanov 2004] and recently to quasi-Polish spaces [de Brecht 2013]. All these spaces are countably-based. Extending descriptive set theory and its effective counterpart to general represented spaces, including non-countably-based spaces has been started in [Pauly, de Brecht ...

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters τi, i = 1, 2, . . . ,K. The characteristic quasipolynomial of such an equation is a multilinear function of e−τis. It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delayper-scalar-chann...

*Correspondence: [email protected] 1Department of Mathematics, Nanchang University, Nanchang, 330031, P.R. China Full list of author information is available at the end of the article Abstract In this paper, we introduce the concept of a quasi-metric-like space, and by defining the w-compatibility of two mappings, we obtain multidimensional coincidence point and multidimensional fixed point th...

Quasi-symmetric 3-designs with block intersection numbers x, y (0 ≤ x ≤ y < k) are studied. It is proved that the parameter λ of a quasi-symmetric 3-(v, k, λ) design satisfies a quadratic whose coefficients are polynomial functions of k, x and y. We use this quadratic to prove that there exist finitely many quasi-symmetric 3-designs under either of the following two restrictions: 1. The block i...

The notion of dislocated quasi metric space was initiated by F. M. Zeyada, G. H. Hassan and M. A. Ahmed[18] in 2006. It is a generalization due to P. Hitzler and A. K. Seda[7] in dislocated metric. Dislocated quasi metric space differs from d islocated metric space with symmetric property. After the establishment of d islocated quasi metric space, it has emerged as important area of research ac...