<abstract>
<title style='display:none'>Abstract</title>
Some inequalities of Hermite-Hadamard type for <italic>GG-</italic>convex functions defined on positive intervals are given. Applications for special means are also provided.
</abstract>

Inequalities of Hermite-Hadamard Type for <italic>GG</italic>-Convex Functions

<abstract><title style='display:none'>Abstract</title> In recent years significant work has been done to use Neural Networks in game AI, and harness the advantages of such a technique. This paper would like to show that it is possible using neuroevolution to evolve a neural network topology optimized for a given task and avoiding over or under complexification by human hands. In order to illustrate this we implement two agents capable of playing simple zero sum perfect information games with the help of the genetic algorithm Neuroevolution of augmenting topologies. To illustrate this optimization we load the resulting topologies onto an Android OS game app. </abstract>

Neuro-evolution in Zero-Sum Perfect Information Games on the Android OS

<abstract><title style='display:none'>Abstract</title> Let G = (V,E) be a simple connected molecular graph. In such a simple molecular graph, vertices represent atoms and edges represent chemical bonds, we denoted the sets of vertices and edges by V = V (G) and E = E(G), respectively. If d(u, ν) be the notation of distance between vertices u, ν ∈ V and is defined as the length of a shortest path connecting them. Then, Eccentricity connectivity polynomial of a molecular graph G is defined as ECP(G, x) = ∑ν∈V dG(ν)xecc(ν), where ecc(ν) is defined as the length of a maximal path connecting to another vertex of v. dG(ν) (or simply dv) is degree of a vertex ν ∈ V (G), and is defined as the number of adjacent vertices with v. In this paper, we focus on the structure of molecular graph circumcoronene series of benzenoid Hk (k ≥ 2) and counting the eccentricity connectivity polynomial ECP(Hk) and eccentricity connectivity index ξ(Hk), by new method (called Ring-cut Method). </abstract>

Computing Eccentricity Connectivity Polynomial of Circumcoronene Series of Benzenoid Hk by Ring-Cut Method

<abstract><title style='display:none'>Abstract</title> In this paper, we prove some sharp maximal function estimates for the commutators related to certain generalized fractional integral operator with general kernel and the BMO and Lipschitz functions. As an application, we obtain the boundedness of the commutators on Lebesgue, Morrey and Triebel-Lizorkin spaces. The operator includes fractional Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.</abstract>

Sharp Maximal Function Estimates and Boundedness for Commutator Related to Generalized Fractional Integral Operator

<abstract>
<title style='display:none'>Abstract</title>
The object of the present paper is to study generalized weakly symmetric and generalized weakly Ricci symmetric Kenmotsu manifolds whose metric tensor is <italic>η</italic>-Ricci soliton. The paper also aims to bring out curvature conditions for which <italic>η-</italic>Ricci solitons in Kenmotsu manifolds are sometimes shrinking or expanding and some other time remain steady. The existence of each generalized weakly symmetric and generalized weakly Ricci symmetric Kenmotsu manifold is ensured by an example.
</abstract>

<italic>η</italic>-Ricci solitons in Kenmotsu manifolds

<abstract>
<title style='display:none'>Abstract</title>
In this paper we show that, if that the function <italic>f</italic> : [0, ∞) → 𝔾 is operator monotone in [0, ∞) then there exist <italic>b</italic> ≥ 0 and a positive measure <italic>m</italic> on [0, ∞) such that <disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_awutm-2022-0008_eq_001.png"/>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:mtable columnalign="left"><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mrow><mml:mrow><mml:mo>[</mml:mo> <mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>B</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>-</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow> <mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mo>-</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mrow><mml:mo>=</mml:mo><mml:mi>b</mml:mi><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mo>-</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:mrow><mml:msubsup><mml:mo>∫</mml:mo><mml:mn>0</mml:mn><mml:mo>∞</mml:mo></mml:msubsup><mml:mrow><mml:msup><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo>[</mml:mo> <mml:mrow><mml:mrow><mml:msubsup><mml:mo>∫</mml:mo><mml:mn>0</mml:mn><mml:mn>1</mml:mn></mml:msubsup><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>[</mml:mo> <mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>t</mml:mi><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:mi>s</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mo>-</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow> <mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mrow></mml:mrow> <mml:mo>]</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>m</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math>
<tex-math>\matrix{ {\left[ {f\left( B \right) - f\left( A \right)} \right]\left( {B - A} \right) = } \hfill \cr { = b{{\left( {B - A} \right)}^2} + \int_0^\infty {{s^2}\left[ {\int_0^1 {{{\left[ {{{\left( {\left( {1 - t} \right)A + tB + s} \right)}^{ - 1}}\left( {B - A} \right)} \right]}^2}dt} } \right]dm\left( s \right)} } \hfill \cr }</tex-math>
</alternatives>
</disp-formula> for all <italic>A, B</italic> &gt; 0. Some necessary and sufficient conditions for the operators <italic>A, B</italic> &gt; 0 such that the inequality <disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_awutm-2022-0008_eq_002.png"/>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>B</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>A</mml:mi><mml:mo>≥</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>B</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:math>
<tex-math>f\left( B \right)B + f\left( A \right)A \ge f\left( A \right)B + f\left( B \right)A</tex-math>
</alternatives>
</disp-formula>
holds for any operator monotone function <italic>f</italic> on [0, ∞) are also given.
</abstract>

Some inequalities for operator monotone functions

<abstract>
<title style='display:none'>Abstract</title>
In this paper, we present a novel class of Copson-type inequalities involving the right-sided <italic>k</italic>-Hadamard fractional integral operator with all parameters of integrability <italic>p</italic> ≠ 0 and obtain some classical special cases of Copson inequalities. The main results will be proved by employing the Hölder inequality and the Fubini theorem.
</abstract>

Copson-type Inequalities via the <italic>k</italic>-Hadamard Operator

<abstract>
<title style='display:none'>Abstract</title>
We identify pointed vortex loops in the plane with low dimensional nonlinear flags decorated with volume forms. We show how submanifolds of such decorated nonlinear flags can be identified with coadjoint orbits of the area pre- serving diffeomorphism group and relate them to coadjoint orbits of pointed vortex loops. The subgroup of the dihedral group preserving the vorticity data plays a role in the description of these coadjoint orbits.
</abstract>

Decorated Nonlinear Flags, Pointed Vortex Loops and the Dihedral Group

<abstract>
<title style='display:none'>Abstract</title>
The aim of this paper is to give sufficient conditions for Ψ − conditional asymptotic stability of the Ψ − bounded solutions of a nonlinear Lyapunov matrix differential equation with integral term as right side.
</abstract>

On the Ψ − Conditional Asymptotic Stability of a Nonlinear Lyapunov Matrix Differential Equation with Integral Term as Right Side

<abstract>
<title style='display:none'>Abstract</title>
This paper discusses the global convergence of successive approximations methods for solving integro-differential equation via resolvent operators in Banach spaces. We prove a theorem on the global convergence of successive approximations to the unique solution of the problems. An example is given to show the application of our result.
</abstract>

Existence and Successive Approximations of Mild Solution for Integro-differential Equations in Banach Spaces

<abstract>
<title style='display:none'>Abstract</title>
The assembly of billions of short sequencing reads into a contiguous genome is a daunting task. The foundation knowledge of current DNA assembly models is concentrated among a select group, where the solution to the genome assembly challenge lies in proper ordering the genomic data. This contribution’s objective is to provide an overview of the original graph models used in DNA sequencing by hybridization. With the updated analytical approach based on the bidirectional bipartite graph class, the theoretical basic structure of the DNA assembly model has been described in new perspective by incorporating few short hypothetical DNA sequences. On the Galaxy platform, by using Spades assembler and Velvet assembler, the comparative outcomes of an experiment are presented, and we also identify their working schemes. Here, the working principle of de Bruijn graph has been discussed in broader point of view.
</abstract>

A Study of Computational Genome Assembly by Graph Theory

<abstract>
<title style='display:none'>Abstract</title>
Along this paper, we study an evolution inclusion governed by the so-called sweeping process. The right side of the inclusion contains a set-valued perturbation, supposed to be the external forces exercised on the system. We prove existence and relaxation results under weak assumptions on the perturbation by taking a truncated Lipschitz condition. These perturbations have non-convex and unbounded values without any compactness condition; we just assume a linear growth assumption on the element of minimal norm. The approach is based on the construction of approximate solutions. The relaxation is obtained by proving the density of the solution set of the original problem in a closure of the solution set of the relaxed one.
</abstract>

Non-convex perturbation to evolution problems involving Moreau’s sweeping process

<abstract><title style='display:none'>Abstract</title> Fuzzy ordered linear spaces, Riesz spaces, fuzzy Archimedean spaces and σ-complete fuzzy Riesz spaces were defined and studied in several works. Following the efforts along this line, we define fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections and establish their fundamental properties. </abstract>

Fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections

<abstract><title style='display:none'>Abstract</title> In this paper, generalized Hirota Satsuma coupled KdV system is solved with tanh method and q-Homotopy analysis method. New fractional derivative definition called “conformable fractional derivative” used in the solution procedure. Tanh method with conformable derivative firstly introduced in the literature. By the graphics of analytical and approximate solutions, it is shown that, both methods provide an effective and powerful mathematical tool for solving nonlinear PDEs containing conformable fractional derivative. </abstract>

On the New Solutions of the Conformable Time Fractional Generalized Hirota-Satsuma Coupled KdV System

<abstract><title style='display:none'>Abstract</title>In this paper, we introduce and study the class of <italic>enriched strictly pseudocontractive mappings</italic> in Hilbert spaces and extend some convergence theorems, i.e., Theorem 12 in [Brow-der, F. E., Petryshyn, W. V., <italic>Construction of fixed points of nonlinear mappings in Hilbert space</italic>, J. Math. Anal. Appl. <bold>20</bold> (1967), 197–228] and Theorem 3.1 in [Marino, G., Xu, H.-K., <italic>Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces</italic>, J. Math. Anal. Appl. <bold>329</bold> (2007), no. 1, 336–346], from the class of strictly pseudocontractive mappings to that of enriched strictly pseudocontractive mappings and thus include many other important related results from literature as particular cases.</abstract>

Weak and strong convergence theorems for the Krasnoselskij iterative algorithm in the class of enriched strictly pseudocontractive operators

<abstract><title style='display:none'>Abstract</title>In this paper, the existence of positive solutions for a nonlinear fourth-order two-point boundary value problem with integral condition is investigated. By using Krasnoselskii’s fixed point theorem on cones, sufficient conditions for the existence of at least one positive solutions are obtained.</abstract>

Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), Department of Mathematics, University of Oran 1 Ahmed Benbella, 31000 Oran,

Department of Physics, University of Sciences and Technology of Oran-MB, El Mnaouar, BP 1505, 31000 Oran, Algeria; Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), Department of Mathematics, University of Oran 1 Ahmed Benbella, 31000 Oran,

Positive Solutions of a Nonlinear Fourth-order Integral Boundary Value Problem

<abstract><title style='display:none'>Abstract</title> In this paper we consider the following problems: (1) Which weakly Picard operators satisfy a retraction- displacement condition? (2) For which weakly Picard operators the fixed point problem is well posed? (3) Which weakly Picard operators have Ostrowski property? Some applications and open problems are also presented. </abstract>

Relevant Classes of Weakly Picard Operators

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