Report of Meeting: 19th International Conference on Functional Equations and Inequalities, B¦dlewo, Poland, September 11–18, 2021

<abstract><title style='display:none'>Abstract</title>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>

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

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

<abstract>
<title style='display:none'>Abstract</title>
 Recently Kanas and Ronning introduced the classes of starlike and convex functions, which are normalized with ƒ(ξ) = ƒ0(ξ) − 1 = 0, ξ (|ξ| = d) is a fixed point in the open disc U = {z ∈ ℂ: |z| &lt; 1}. In this paper we define a new subclass of starlike functions of complex order based on q-hypergeometric functions and continue to obtain coefficient estimates, extreme points, inclusion properties and neighbourhood results for the function class T Sξ(α, β,γ). Further, we obtain integral means inequalities for the function ƒ ∈ T Sξ(α, β,γ). 
</abstract>

Starlike functions of complex order involving q-hypergeometric functions with fixed point

<abstract><title style='display:none'>Abstract</title>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><title style='display:none'>Abstract</title>In this paper, we define a new subclass of bi-univalent functions involving <italic>q</italic>-difference operator in the open unit disk. For functions belonging to this class, we obtain estimates on the first two Taylor-Maclaurin coefficients <italic>|a</italic>2<italic>|</italic> and <italic>|a</italic>3<italic>|</italic>.</abstract>

Bi-Bazilevič functions of complex order involving Ruscheweyh type <italic>q</italic>-difference operator

<abstract>
<title style='display:none'>Abstract</title>
The aim of this article is to introduce the concept of centrally-extended Jordan epimorphisms and proving that if <italic>R</italic> is a non-commutative prime ring (∗-ring) of characteristic not two, and <italic>G</italic> is a CE-Jordan epimorphism such that [<italic>G</italic>(<italic>x</italic>), <italic>x</italic>] ∈ <italic>Z</italic>(<italic>R</italic>) ([<italic>G</italic>(<italic>x</italic>), <italic>x</italic>∗] ∈ <italic>Z</italic>(<italic>R</italic>)) for all <italic>x</italic> ∈ <italic>R</italic>, then <italic>R</italic> is an order in a central simple algebra of dimension at most 4 over its center or there is an element <italic>λ</italic> in the extended centroid of <italic>R</italic> such that <italic>G</italic>(<italic>x</italic>) = <italic>λx</italic> (<italic>G</italic>(<italic>x</italic>) = <italic>λx</italic>∗) for all <italic>x</italic> ∈ <italic>R</italic>.
</abstract>

Rings with centrally-extended Jordan epimorphisms

<abstract>
<title style='display:none'>Abstract</title>
By rewriting the differential entropy in a form of a differ-integral function’s limit, and deforming the ordinary derivative to a fractional-order one, we derive in this paper a novel generalized fractional-order differential entropy along with its related information measures. When the order of fractional differentiation <italic>α</italic> → 1, the ordinary Shannon’s differential entropy is recovered, which corresponds to the results from first-order ordinary differentiation.
</abstract>

Some theoretical results on fractional-order continuous information measures

<abstract>
<title style='display:none'>Abstract</title>
In this note we provide a complete classification of weak combinatorics of the so-called maximizing line arrangements in the complex projective plane.
</abstract>

On maximizing line arrangements in the complex plane

<italic>Report of Meeting</italic>: 20th International Conference on Functional Equations and Inequalities, Będlewo, Poland, September 17–23, 2023

<abstract>
<title style='display:none'>Abstract</title>
In the present paper, a theorem on <italic>θ</italic> −|<italic>T; δ</italic>|k summability method of an infinite series is proved, and also by using this method, a result on summability of a trigonometric Fourier series is obtained.
</abstract>

On absolute summability of infinite series and Fourier series

<abstract>
<title style='display:none'>Abstract</title>
The present paper deals with some existence results for the Darboux problem of partial fractional random differential equations with finite delay. The arguments are based on a random fixed point theorem with stochastic domain combined with the measure of noncompactness. An illustration is given to show the applicability of our results.
</abstract>

Some new existence results for fractional partial random nonlocal differential equations with delay

<abstract><title style='display:none'>Abstract</title>In this paper we study existence and uniqueness of solutions for a coupled system consisting of fractional differential equations of Caputo type, subject to Riemann–Liouville fractional integral boundary conditions. The uniqueness of solutions is established by Banach contraction principle, while the existence of solutions is derived by Leray–Schauder’s alternative. We also study the Hyers–Ulam stability of mentioned system. At the end, examples are also presented which illustrate our results.</abstract>

Existence and stability analysis of nonlinear sequential coupled system of Caputo fractional differential equations with integral boundary conditions

Conference on Ulam’s Type Stability Rytro, Poland, June 2-6, 2014

<abstract><title style='display:none'>Abstract</title>In this paper, we derive several subordination results and integral means result for certain class of analytic functions defined by means of <italic>q</italic>-differential operator. Some interesting corollaries and consequences of our results are also considered.</abstract>

A subordination results for a class of analytic functions defined by <italic>q</italic>-differential operator

<abstract>
<title style='display:none'>Abstract</title>
 In the paper based on the question of Zhang and Lü [15], we present one theorem which will improve and extend results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].
</abstract>

Further investigations on a question of Zhang and Lü

<abstract><title style='display:none'>Abstract</title>In this paper, we study <italic>∗</italic>-g-frames in tensor products of Hilbert <italic>C∗</italic>-modules. We show that a tensor product of two <italic>∗</italic>-g-frames is a <italic>∗</italic>-g-frame, and we get some result.</abstract>

*-g-frames in tensor products of Hilbert <italic>C*</italic>-modules

<abstract><title style='display:none'>Abstract</title>In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam–Hyers stability, generalized Ulam– Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers– Rassias stability of the solution to an implicit nonlinear fractional differential equations corresponding to an implicit integral boundary condition. We develop conditions for the existence and uniqueness by using the classical fixed point theorems such as Banach contraction principle and Schaefer’s fixed point theorem. For stability, we utilize classical functional analysis. The main results are well illustrated with an example.</abstract>

Stability analysis of implicit fractional differential equation with anti–periodic integral boundary value problem

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