Some Novel Fractional Integral Inequalities over a New Class of Generalized Convex Function

The comprehension of inequalities in convexity is very important for fractional calculus and its effectiveness in many applied sciences. In this article, we handle a novel investigation that depends on the Hermite–Hadamard-type inequalities concerning a monotonic increasing function. The proposed methodology deals with a new class of convexity and related integral and fractional inequalities. There exists a solid connection between fractional operators and convexity because of its fascinating nature in the numerical sciences. Some special cases have also been discussed, and several already-known inequalities have been recaptured to behave well. Some applications related to special means, q-digamma, modified Bessel functions, and matrices are discussed as well. The aftereffects of the plan show that the methodology can be applied directly and is computationally easy to understand and exact. We believe our findings generalise some well-known results in the literature on s-convexity.

New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulas

In this paper, the authors derive some new generalizations of fractional trapezium-like inequalities using the class of harmonic convex functions. Moreover, three new fractional integral identities are given, and on using them as auxiliary results some interesting integral inequalities are found. Finally, in order to show the efficiency of our main results, some applications to special means for different positive real numbers and error estimations for quadrature formulas are obtained.

Fractional Integral Inequalities for Some Convex Functions

In this paper, we obtained several new integral inequalities using fractional Riemann-Liouville integrals for convex s-Godunova-Levin functions in the second sense and for quasi-convex functions. The results were gained by applying the double Hermite-Hadamard inequality, the classical Holder inequalities, the power mean, and weighted Holder inequalities. In particular, the application of the results for several special computing facilities is given. Some applications to special means for arbitrary real numbers: arithmetic mean, logarithmic mean, and generalized log-mean, are provided.

Schur-Convexity for Elementary Symmetric Composite Functions and Their Inverse Problems and Applications

This paper investigates the Schur-convexity, Schur-geometric convexity, and Schur-harmonic convexity for the elementary symmetric composite function and its dual form. The inverse problems are also considered. New inequalities on special means are established by using the theory of majorization.

The Key Elements of the Guarantee System of Compliance with the Legitimate Interests of the Parties to Investment Transactions: Interdependence and Functions

Introduction: the relevance of the research is due to the transformation of social relations in the neoindustrial era, which opens up technological innovations to mankind. In this regard, there is an objective need to revise and modernize many legal institutions and create a new legislative matter for the normal functioning of the banking and investment sector adequate to modern realities. Purpose: the paper contributes to the formation of the understanding of individual investors, recipients of investments, and investment intermediaries of the fact that there is a set of special means that can be freely implemented in a situation of violation of the rights and noncompliance with the legitimate interests of each of the participants in these relations. These special means should represent the interrelated and interdependent elements of the system, reinforcing, complementing each other, thereby forming a synergistic effect and thereby providing these guarantees. Methods: the methodological framework for the conducted scientific research is the method of historical materialism. In addition, while writing the paper, both the traditional general scientific methods (the dialectical method of cognition, analysis, synthesis, induction, deduction, etc.) and the specific scientific legal methods (formal-legal, the method of legal interpretation, etc.) were used. Results: the author substantiates the existence of five functional elements that guarantee in their totality a system of guarantees of compliance with the legitimate interests of participants to remote digital investment transactions. Firstly, there is a developed civil law regulation. Secondly, a workable institution of the financial Ombudsman. Thirdly, the effective regulation of this market segment by the central bank. Fourthly, jurisdictional and non-jurisdictional justice operating within the framework of legality. Fifthly, advanced information technologies for transactions and protection of rights. The functioning of the designated system of guarantees is investigated by elements. Conclusions: in summary, it is concluded that the efforts of scientists and developers-practitioners should be aimed at creating an end-to-end technology for participation in remote digital investment transactions and protection of their rights by the parties. The necessity of introducing special service applications that make up such technology is argued. It is proved that the implementation of such technology will allow functioning effectively, mutually complementing and strengthening all the elements of the guarantee system. It is proved that the key idea underlying the end-to-end technology of participation in remote digital investment transactions is the execution of the transactions themselves in the mode of smart contracts, which are executed, and the facts about the execution of their stages are stored in the distributed registry system. At the same time, this information technology should be integrated with the hardware and software complex of the GOSUSLUGI portal as a special service presented in the personal account of a citizen, as well as with the website of the Federal Tax Service with the corresponding service in the personal account of a party – a legal entity. These services should provide for a guaranteed and unhindered (automatic) possibility of an electronic, legally significant, appeal by a party to a remote digital investment transaction to the Bank of Russia, to a financial commissioner, to an arbitration institution, to a court.

MATHEMATICAL MODEL OF UNDERWATER DEMINING BY DIPPER DIVERS OF THE SESU

It is shown that the problem of improving the effectiveness of prevention of emergencies related to the underwater location of explosive objects is relevant. An important and unresolved part of the problem is the lack of a mathematical model of the emergency response process associated with the underwater location of an explosive device in general. Based on this, the object of the study was the elimination of an emergency situation related to the underwater location of explosive objects, and the subject of the study – the process of operational activities of personnel of the underwater demining department of a group of special diving rescue team. The aim of the work is to develop a mathematical model of the emergency response process related to the underwater location of an explosive object as a process of functioning of the system "emergency – special means of underwater demining – diver-sapper", which should be the basis for substantiation of operational and technical recommendations. increasing the efficiency of underwater demining by diver sappers without reducing their level of safety. It is shown that the mathematical model of underwater demining by a diver-sapper is a system of three analytical dependences. The first is a functional that describes the process of underwater demining in the form of a three-factor polynomial model. The second allows us to present this functionality as a set of one-factor models. The third provides the definition of weights in solving a multifactor problem. It is noted that such a model allows to proceed to the substantiation of operational and technical recommendations to the management of the group of special diving works. The advantage of the new scientific result is the ability to obtain both quantitative estimates of the impact of the direct components of the system "diver-sapper – special means of underwater demining – underwater location of an explosive object" and their relationship. The disadvantage is the large number of experimental results that must be obtained to implement the selected plan.

Some new inequalities for convex functions via generalized integral operators and their applications

The authors discover an identity for a generalized integral operator via differentiable function. By using this integral equation, we derive some new bounds on Hermite–Hadamard type integral inequality for differentiable mappings that are in absolute value at certain powers convex. Our results include several new and known results as particular cases. At the end, some applications of presented results for special means and error estimates for the mixed trapezium and midpoint formula have been analyzed. The ideas and techniques of this paper may stimulate further research in the field of integral inequalities.

New Parameterized Inequalities for η-Quasiconvex Functions via (p, q)-Calculus

In this work, first, we consider novel parameterized identities for the left and right part of the (p,q)-analogue of Hermite–Hadamard inequality. Second, using these new parameterized identities, we give new parameterized (p,q)-trapezoid and parameterized (p,q)-midpoint type integral inequalities via η-quasiconvex function. By changing values of parameter μ∈[0,1], some new special cases from the main results are obtained and some known results are recaptured as well. Finally, at the end, an application to special means is given as well. This new research has the potential to establish new boundaries in comparative literature and some well-known implications. From an application perspective, the proposed research on the η-quasiconvex function has interesting results that illustrate the applicability and superiority of the results obtained.

New Integral Inequalities via Generalized Preinvex Functions

The theory of convexity plays an important role in various branches of science and engineering. The objective of this paper is to introduce a new notion of preinvex functions by unifying the n-polynomial preinvex function with the s-type m–preinvex function and to present inequalities of the Hermite–Hadamard type in the setting of the generalized s-type m–preinvex function. First, we give the definition and then investigate some of its algebraic properties and examples. We also present some refinements of the Hermite–Hadamard-type inequality using Hölder’s integral inequality, the improved power-mean integral inequality, and the Hölder-İşcan integral inequality. Finally, some results for special means are deduced. The results established in this paper can be considered as the generalization of many published results of inequalities and convexity theory.

EXPERIENCE OF FOREIGN COUNTRIES IN THE FIELD OF ORGANIZING ACTIVITIES FOR THE PROTECTION OF PUBLIC ORDER WITH SERVICE DOGS

В статье рассматривается такой вид специальных средств, как служебные собаки, которые используются сотрудниками правоохранительных органов зарубежных стран при охране общественного порядка. This article addresses the type of special means such as service dogs, which are used by law enforcement officers of foreign countries in public order. There were analyzed cases of their use by various law enforcement agencies in consideration of this topic.