<abstract xmlns="http://www.w3.org/1999/xhtml">The aim of this article is to provide the local convergence analysis of two novel competing sixth convergence order methods for solving equations involving Banach space valued operators. Earlier studies have used hypotheses reaching up to the sixth derivative but only the first derivative appears in these methods. These hypotheses limit the applicability of the methods. That is why we are motivated to present convergence analysis based only on the first derivative. Numerical examples where the convergence criteria are tested are provided. It turns out that in these examples the criteria in the earlier works are not satisfied, so these results cannot be used to solve equations but our results can be used.</abstract>

Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka

Local convergence comparison between two novel sixth order methods for solving equations

<abstract xmlns="http://www.w3.org/1999/xhtml">This article presents the theory of focal locus applied to the hyper-surfaces in the projective space which are (finitely) covered by linear spaces and such that the tangent space is constant along these spaces.</abstract>

Dipartimento di Scienze Matematiche, Informatiche e Fisiche

Università degli Studi di Udine via delle Scienze

Dipartimento di Matematica e Applicazioni

Università degli Studi di Napoli “Federico II”

On the hypersurfaces contained in their Hessian

<abstract xmlns="http://www.w3.org/1999/xhtml">In this article, we define multi-invertible, multivalued maps. These mappings are a natural generalization of <italic>r</italic>-maps (in particular, the singlevalued invertible maps). They have many interesting properties and applications. In this article, the multi-invertible maps are applied to the construction of morphisms and to the theory of coincidence.</abstract>

Multi-invertible maps and their applications

<abstract xmlns="http://www.w3.org/1999/xhtml">In this note the necessary and sufficient condition it would the concomitant of the geometric object was the geometric object too is given.</abstract>

On the geometric concomitants

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, a known result dealing with | ̄<italic>N, pn</italic>|<italic>k</italic> summability of infinite series has been generalized to the φ − | ̄<italic>N, pn</italic>; δ|<italic>k</italic> summability of infinite series by using an almost increasing sequence.</abstract>

A new application of almost increasing sequences

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we establish some fractional Hermite-Hadamard type integral inequalities for functions whose modulus of the mixed derivatives are co-ordinated <italic>s</italic>-preinvex in the second sense.</abstract>

Faculté des Sciences et de la Technologie

Fractional Hermite-Hadamard type integral inequalities for functions whose modulus of the mixed derivatives are co-ordinated <italic>s</italic>-preinvex in the second sense

<abstract xmlns="http://www.w3.org/1999/xhtml">In the present paper, two theorems of absolute summability have been proved by using the definition of almost increasing sequence.</abstract>

New results for almost increasing sequences

<abstract xmlns="http://www.w3.org/1999/xhtml">We present a description of all binomial sequences of polynomials in one variable over a field of characteristic zero.</abstract>

Binomial sequences

<abstract xmlns="http://www.w3.org/1999/xhtml">The object of the present paper is to investigate the nature of Ricci solitons on <italic>D</italic>-homothetically deformed Kenmotsu manifold with generalized weakly symmetric and generalized weakly Ricci symmetric curvature restrictions.</abstract>

Ricci solitons in a generalized weakly (Ricci) symmetric <italic>D</italic>-homothetically deformed Kenmotsu manifold

<abstract xmlns="http://www.w3.org/1999/xhtml">To date, many identities of different quaternions, including the Fibonacci and Lucas quaternions, have been investigated. In this study, we present Gelin-Cesáro identities for Fibonacci and Lucas quaternions. The identities are a worthy addition to the literature. Moreover, we give Catalan’s identity for the Lucas quaternions.</abstract>

Gelin-Cesáro identities for Fibonacci and Lucas quaternions

<abstract xmlns="http://www.w3.org/1999/xhtml">L. Losonczi [4] determined local solutions of the generalized Cauchy equation <italic>f</italic>(<italic>F</italic> (<italic>x, y</italic>)) = <italic>f</italic>(<italic>x</italic>) + <italic>f</italic>(<italic>y</italic>) on components of the definition of a given associative rational function <italic>F.</italic> The class of the associative rational function was described by A. Chéritat [1] and his work was followed by paper [3] of the author. The aim of the present paper is to describe local solutions of the equation considered for some singular associative rational functions.</abstract>

Cauchy type functional equations related to some associative rational functions

<abstract xmlns="http://www.w3.org/1999/xhtml">The idea presented here of a general quantization rule for bound states is mainly based on the Riccati equation which is a result of the transformed, time-independent, one-dimensional Schrödinger equation. The condition imposed on the logarithmic derivative of the ground state function <italic>W</italic>0 allows to present the Riccati equation as the unit circle equation with winding number equal to one which, by appropriately chosen transformations, can be converted into the unit circle equation with multiple winding number. As a consequence, a completely new quantization condition, which gives exact results for any quantum number, is obtained.</abstract>

Solutions of the time-independent Schrödinger equation by uniformization on the unit circle

<italic>Report of Meeting</italic> 18th International Conference on Functional Equations and Inequalities, Będlewo, Poland, June 9–15, 2019

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Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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