<abstract xmlns="http://www.w3.org/1999/xhtml">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

<abstract xmlns="http://www.w3.org/1999/xhtml">We present both necessary and sufficient conditions for a convex closed shape such that for every convex function the average integral over the shape does not exceed the average integral over its boundary.It is proved that this inequality holds for <italic>n</italic>-dimensional parallelotopes, <italic>n-</italic>dimensional balls, and convex polytopes having the inscribed sphere (tangent to all its facets) with the centre in the centre of mass of its boundary.</abstract>

Jensen-type geometric shapes

<abstract xmlns="http://www.w3.org/1999/xhtml">In this short note, we give some counter examples which show that [11, Proposition 3.5] is not true. As a consequence, the arguments in [11, Proposition 4.10] are not valid.</abstract>

Counter examples for pseudo-amenability of some semigroup algebras

<abstract xmlns="http://www.w3.org/1999/xhtml">We prove that certain Fano fourfolds of K3 type constructed by Fatighenti–Mongardi have a multiplicative Chow–Künneth decomposition. We present some consequences for the Chow ring of these fourfolds.</abstract>

On the Chow ring of certain Fano fourfolds

<abstract xmlns="http://www.w3.org/1999/xhtml">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 xmlns="http://www.w3.org/1999/xhtml">Let <italic>f</italic> be a polynomial in two complex variables. We say that <italic>f</italic> is nearly irreducible if any two nonconstant polynomial factors of <italic>f</italic> have a common zero in C2. In the paper we give a criterion of nearly irreducibility for a given polynomial <italic>f</italic> in terms of its Newton diagram.</abstract>

Nearly irreducibility of polynomials and the Newton diagrams

<abstract xmlns="http://www.w3.org/1999/xhtml">This paper presents some generalizations of BCI algebras (the RM, tRM, *RM, RM**, *RM**, aRM**, *aRM**, BCH**, BZ, pre-BZ and pre-BCI algebras). We investigate the p-semisimple property for algebras mentioned above; give some examples and display various conditions equivalent to p-semisimplicity. Finally, we present a model of mereology without antisymmetry (NAM) which could represent a tRM algebra.</abstract>

Siedlce University of Natural Sciences and Humanities

The p-semisimple property for some generalizations of BCI algebras and its applications

<abstract xmlns="http://www.w3.org/1999/xhtml">This paper presents a theorem dealing with absolute matrix summability of infinite series. This theorem has been proved taking quasi <italic>β</italic>-power increasing sequence instead of almost increasing sequence.</abstract>

A new result on the quasi power increasing sequences

<abstract xmlns="http://www.w3.org/1999/xhtml">In the present paper, we study in the harmonic analysis associated to the Weinstein operator, the boundedness on <italic>L</italic><italic>p</italic> of the uncentered maximal function. First, we establish estimates for the Weinstein translation of characteristic function of a closed ball with radius <italic>ɛ</italic> centered at 0 on the upper half space ℝd–1× ]0, +∞ [. Second, we prove weak-type <italic>L</italic>1-estimates for the uncentered maximal function associated with the Weinstein operator and we obtain the <italic>L</italic><italic>p</italic>-boundedness of this operator for 1 &lt; <italic>p</italic> ≤ + ∞. As application, we define a large class of operators such that each operator of this class satisfies these <italic>L</italic><italic>p</italic>-inequalities. In particular, the maximal operator associated respectively with the Weinstein heat semigroup and the Weinstein-Poisson semigroup belong to this class.</abstract>

Maximal functions for Weinstein operator

<abstract xmlns="http://www.w3.org/1999/xhtml">The <italic>n</italic>-tuples of commuting Hilbert space contractions are considered. We give a model of a commuting lifting of one contraction and investigate conditions under which a commuting lifting theorem holds for an <italic>n</italic>-tuple. A series of such liftings leads to an isometric dilation of the <italic>n</italic>-tuple. The method is tested on some class of triples motivated by Parrotts example. It provides also a new proof of the fact that a positive definite <italic>n</italic>-tuple has an isometric dilation.</abstract>

On dilation and commuting liftings of <italic>n</italic>-tuples of commuting Hilbert space contractions

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we introduce multi-Jensen-cubic mappings and unify the system of functional equations defining the multi-Jensen-cubic mapping to a single equation. Applying a fixed point theorem, we establish the generalized Hyers-Ulam stability of multi-Jensen-cubic mappings. As a known outcome, we show that every approximate multi-Jensen-cubic mapping can be multi-Jensen-cubic.</abstract>

Department of Mathematics, South Tehran Branch

Department of Mathematics, Garmsar Branch

Approximate multi-Jensen-cubic mappings and a fixed point theorem

<abstract xmlns="http://www.w3.org/1999/xhtml">In this work, we construct the sequence spaces <italic>f</italic>(<italic>Q</italic>(<italic>r, s, t, u</italic>)), <italic>f</italic>0(<italic>Q</italic>(<italic>r, s, t, u</italic>)) and <italic>fs</italic>(<italic>Q</italic>(<italic>r, s, t, u</italic>)), where <italic>Q</italic>(<italic>r, s, t, u</italic>) is quadruple band matrix which generalizes the matrices Δ3, <italic>B</italic>(<italic>r, s, t</italic>), Δ2, <italic>B</italic>(<italic>r, s</italic>) and Δ, where Δ3, <italic>B</italic>(<italic>r, s, t</italic>), Δ2, <italic>B</italic>(<italic>r, s</italic>) and Δ are called third order difference, triple band, second order difference, double band and difference matrix, respectively. Also, we prove that these spaces are <italic>BK</italic>-spaces and are linearly isomorphic to the sequence spaces <italic>f</italic>, <italic>f</italic>0 and <italic>fs</italic>, respectively. Moreover, we give the Schauder basis and <italic>β</italic>, γ-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.</abstract>

Almost convergent sequence spaces derived by the domain of quadruple band matrix

<abstract xmlns="http://www.w3.org/1999/xhtml">In this article we present the existence and uniqueness results for fractional integro-differential equations with <italic>ψ</italic>-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss <italic>E</italic>α -Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of the <italic>δ</italic>-approximate solution.</abstract>

Dr Babasaheb Ambedkar Marathwada University

Existence results of <italic>ψ</italic>-Hilfer integro-differential equations with fractional order in Banach space

<abstract xmlns="http://www.w3.org/1999/xhtml">This scientific note relates to introducing certain elementary operators defined in the unit disk in the complex plane, then determining various applications (specified by those operators) to certain analytic functions, and also revealing a number of possible implications of them.</abstract>

A note on some elementary properties and applications of certain operators to certain functions analytic in the unit disk

<abstract xmlns="http://www.w3.org/1999/xhtml">The aim of this paper is to prove the existence and stability of solutions of a system of quadratic integral equations in the Banach algebra of continuous and bounded functions on unbounded rectangle. The main tool used in our considerations is the multiple fixed point theorem which is a consequence of Darbo’s fixed point theorem and the technique associated with measures of noncompactness. We also present an illustrative example.</abstract>

Existence and stability of solutions for a system of quadratic integral equations in Banach algebras

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Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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