<abstract xmlns="http://www.w3.org/1999/xhtml">Recently, Haji Mohd and Darus [<xref ref-type="bibr" rid="j_aupcsm-2017-0001_ref_001_w2aab3b7ab1b6b1ab1ab1Aa">1</xref>] revived the study of coefficient problems for univalent functions associated with quasi-subordination. Inspired largely by this article, we provide coefficient estimates with <italic>k</italic>-th root transform for certain subclasses of 𝒮 defined by quasi-subordination.</abstract>

Post-Graduate and Research Department of Mathematics, Government Arts College for Men

Department of Mathematics, Government First Grade College

Fekete-Szegö inequalities associated with <italic>k</italic>th root transformation based on quasi-subordination

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we discuss the no-arbitrage condition in a discrete financial market model which does not hold the same interest rate assumptions. Our research was based on, essentially, one of the most important results in mathematical finance, called the Fundamental Theorem of Asset Pricing. For the standard approach a risk-free bank account process is used as numeraire. In those models it is assumed that the interest rates for borrowing and saving money are the same. In our paper we consider the model of a market (with <italic>d</italic> risky assets), which does not hold the same interest rate assumptions. We introduce two predictable processes for modelling deposits and loans. We propose a new concept of a martingale pair for the market and prove that if there exists a martingale pair for the considered market, then there is no arbitrage opportunity. We also consider special cases in which the existence of a martingale pair is necessary and the sufficient conditions for these markets to be arbitrage free.</abstract>

Institute of Mathematics, Faculty of Mathematics and Computer Science

Discrete-time market models from the small investor point of view and the first fundamental-type theorem

<abstract xmlns="http://www.w3.org/1999/xhtml">This paper is devoted to the study of a multi-step method with divided differences for solving nonlinear equations in Banach spaces. In earlier studies, hypotheses on the Fréchet derivative up to the sixth order of the operator under consideration is used to prove the convergence of the method. That restricts the applicability of the method. In this paper we extended the applicability of the sixth-order multi-step method by using only hypotheses on the first derivative of the operator involved. Our convergence conditions are weaker than the conditions used in earlier studies. Numerical examples where earlier results cannot be applied to solve equations but our results can be applied are also given in this study.</abstract>

Department of Mathematical and Computational Sciences, NIT Karnataka

Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivative

<abstract xmlns="http://www.w3.org/1999/xhtml">The first result in partition relations topic belongs to Ramsey (1930). Since that this topic has been still explored. Probably the most famous partition theorem is Erdös-Rado theorem (1956). On the other hand in 60’s of the last century Efimov introduced strong sequences method, which was used for proving some famous theorems in dyadic spaces. The aim of this paper is to generalize theorem on strong sequences and to show that it is equivalent to generalized version of well-known Erdös-Rado theorem. It will be also shown that this equivalence holds for singulars. Some applications and conclusions will be presented too.</abstract>

Strong sequences and partition relations

<abstract xmlns="http://www.w3.org/1999/xhtml">The notions of a dual pseudo-Q algebra and a dual pseudo-QC algebra are introduced. The properties and characterizations of them are investigated. Conditions for a dual pseudo-Q algebra to be a dual pseudo-QC algebra are given. Commutative dual pseudo-QC algebras are considered. The interrelationships between dual pseudo-Q/QC algebras and other pseudo algebras are visualized in a diagram.</abstract>

Department of Pure Mathematics, Faculty of Mathematics and Computer

Faculty of Science, Institute of Mathematics and Physic

Some results on pseudo-Q algebras

<abstract xmlns="http://www.w3.org/1999/xhtml">In this note we present a new method for determining the roots of a quartic polynomial, wherein the curve of the given quartic polynomial is intersected by the curve of a quadratic polynomial (which has two unknown coefficients) at its root point; so the root satisfies both the quartic and the quadratic equations. Elimination of the root term from the two equations leads to an expression in the two unknowns of quadratic polynomial. In addition, we introduce another expression in one unknown, which leads to determination of the two unknowns and subsequently the roots of quartic polynomial.</abstract>

Intersect a quartic to extract its roots

<abstract xmlns="http://www.w3.org/1999/xhtml">In the present paper, we define a notion of an m2-topological space by introducing a count of openness of a multiset (mset in short) and study the properties of m2-subspaces, mgp-maps etc. Decomposition theorems involving m-topologies and m2-topologies are established. The behaviour of the functional image and functional preimage of an m2-topologies, the continuity of the identity mapping and a constant mapping in m2-topologies are also examined.</abstract>

On type-2 m-topological spaces

<abstract xmlns="http://www.w3.org/1999/xhtml">We define and study some simple structures which we call <italic>likens</italic> and which are conceptually near to <italic>both</italic> sets of natural numbers, i.e. ℕ with addition and ℕ* = ℕ \ {0} with multiplication. It appears that there are many different likens, which makes it possible to look on usual natural numbers from a more general point of view. In particular, we show that ℕ and ℕ* are related to some functionals on the <italic>space of likens</italic>. A similar idea is known for a long time as <italic>the Beurling generalized numbers</italic>. Our approach may be considered as a little more natural and more general, since it admits the <italic>finitely generated likens</italic>.</abstract>

Likeℕ’s – a point of view on natural numbers

<abstract xmlns="http://www.w3.org/1999/xhtml">A connection between the continuous translation equation and the Jordan non-measurable continuous functions is given.</abstract>

Translation equation and the Jordan non-measurable continuous functions

<italic>Report of Meeting</italic>: 17th International Conference on Functional Equations and Inequalities, Będlewo, Poland, July 9–15, 2017

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Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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