Inclusion Problem Research Articles

Conformable evolution inclusions with causal operators

In this paper, we study local and nonlocal problems of conformable semilinear evolution inclusions with causal operators, which include time lag system and a large classes of parabolic multivalued differential equations. We first investigate the problems with the help of measure of noncompactness and afterwards when the right-hand side is Lipschitz.

On some spectral properties of nonlocal boundary-value problems for nonlinear differential inclusion

UDC 517.9 We study the solutions to the Sturm–Liouville boundary-value problem for a nonlinear differential inclusion with nonlocal conditions. The maximal and minimal solutions are demonstrated. The analysis of eigenvalues and eigenfunctions is performed. It is discussed whether multiple solutions may exist for the inhomogeneous Sturm–Liouville boundary-value problem for differential equation with nonlocal conditions.

Nonmonotone Spectral Analysis for Variational Inclusions

Gradient descent algorithms perform well in convex optimization but can get tied for finding local minima in non-convex optimization. A robust method that combines a spectral approach with nonmonotone line search strategy for solving variational inclusion problems is proposed. Spectral properties using eigenvalues information are used for accelerating the convergence. Nonmonotonic behaviour is exhibited to relax descent property and escape local minima. Nonmonotone spectral conditions leverage adaptive search directions and global convergence for the proposed spectral subgradient algorithm.

Refined Iterative Method for a Common Variational Inclusion and Common Fixed-Point Problem with Practical Applications

This paper introduces a novel parallel method for solving common variational inclusion and common fixed-point (CVI-CFP) problems. The proposed algorithm provides a strong convergence theorem established under specific conditions associated with the CVI-CFP problem. Numerical simulations demonstrate the algorithm’s efficacy in the context of signal recovery problems involving various types of blurred filters. The results highlight the algorithm’s potential for practical applications in image processing and other fields.

Solution of Mismatched Monotone+Lipschitz Inclusion Problems

Solution of Mismatched Monotone+Lipschitz Inclusion Problems

Digital Inclusion Strategy in Modern Cultural Industries through the Prism of Digital Divide

The purpose of the article is to reveal the features of digital inclusion in modern cultural industries of Ukraine and to outline promising strategies for overcoming the digital divide. Research methodology. The analytical method, the method of analysis and synthesis, the dialogical method, the typological method, the systematic method, the method of comparative analysis and the method of scientific generalisation are applied. Scientific novelty. The problem of digital inclusion in the cultural industry has been studied; the theory of digital inclusion in foreign scientific works is considered; the peculiarities of digital inclusion in modern cultural industries of Ukraine were revealed; promising measures on which the strategy for overcoming the digital divide should be based are outlined. Conclusions. The strategy of digital inclusion of cultural industries in Ukraine should be based on a set of measures aimed at overcoming the digital divide, which includes, first of all: providing high-speed Internet to as large a part of the population as possible; all kinds of assistance in the process of improving the digital literacy of potential consumers of a cultural product / service; provision of high-quality technical support; creation of specialised applications and online content, according to the specifics of the activities covered by each cultural industry. Potential forward-looking steps include providing ongoing support to users, reducing professional jargon and offering interpretive resources, and ensuring that technology and training are offered to all users on an equal basis, not just those confident enough to seek help. The study revealed that at the current stage in Ukraine, only libraries not only offer the Internet, but also provide a range of training services from basic digital literacy to the skills needed to use certain services (audio/video streaming service, file sharing services, online platforms), devices and applications that are currently actively used in the system of cultural industries (for example, applications of augmented reality in museum, exhibition activities, performing arts).

Primal-Dual Extrapolation Methods for Monotone Inclusions Under Local Lipschitz Continuity

In this paper, we consider a class of monotone inclusion (MI) problems of finding a zero of the sum of two monotone operators, in which one operator is maximal monotone, whereas the other is locally Lipschitz continuous. We propose primal-dual (PD) extrapolation methods to solve them using a point and operator extrapolation technique, whose parameters are chosen by a backtracking line search scheme. The proposed methods enjoy an operation complexity of [Formula: see text] and [Formula: see text], measured by the number of fundamental operations consisting only of evaluations of one operator and resolvent of the other operator, for finding an ε-residual solution of strongly and nonstrongly MI problems, respectively. The latter complexity significantly improves the previously best operation complexity [Formula: see text]. As a byproduct, complexity results of the primal-dual extrapolation methods are also obtained for finding an ε-KKT or ε-residual solution of convex conic optimization, conic constrained saddle point, and variational inequality problems under local Lipschitz continuity. We provide preliminary numerical results to demonstrate the performance of the proposed methods. Funding: This work was partially supported by the National Science Foundation [Grant IIS-2211491], the Office of Naval Research [Grant N00014-24-1-2702], and the Air Force Office of Scientific Research [Grant FA9550-24-1-0343].

Double Tseng’s Algorithm with Inertial Terms for Inclusion Problems and Applications in Image Deblurring

In this research paper, we present a novel theoretical technique, referred to as the double Tseng’s algorithm with inertial terms, for finding a common solution to two monotone inclusion problems. Developing the double Tseng’s algorithm in this manner not only comprehensively expands theoretical knowledge in this field but also provides advantages in terms of step-size parameters, which are beneficial for tuning applications and positively impact the numerical results. This new technique can be effectively applied to solve the problem of image deblurring and offers numerical advantages compared to some previously related results. By utilizing certain properties of a Lipschitz monotone operator and a maximally monotone operator, along with the identity associated with the convexity of the quadratic norm in the framework of Hilbert spaces, and by imposing some constraints on the scalar control conditions, we can achieve weak convergence to a common zero point of the sum of two monotone operators. To demonstrate the benefits and advantages of this newly proposed algorithm, we performed numerical experiments to measure the improvement in the signal–to–noise ratio (ISNR) and the structural similarity index measure (SSIM). The results of both numerical experiments (ISNR and SSIM) demonstrate that our new algorithm is more efficient and has a significant advantage over the relevant preceding algorithms.

An existence of the solution for generalized system of fractional q-differential inclusions involving p-Laplacian operator and sequential derivatives

In this paper, we investigate the presence of positive solutions for system of fractional q-differential inclusions involving sequential derivatives with respect to the p-Laplacian operator. By using fixed point technique we obtain a new solution for inclusion or boundary value problems with special integral and derivative conditions. At the end, we give an example to show the effect of the solution of this device. The conclusion is expressed to introduce future works.

Local boundedness of weak solutions to an inclusion problem in Musielak–Orlicz–Sobolev spaces

Local boundedness of weak solutions to an inclusion problem in Musielak–Orlicz–Sobolev spaces

Problems of digital inclusion in vocational (vocation-technical) education institutions

Problems of digital inclusion in vocational (vocation-technical) education institutions

On set-valued fixed points, their geometry and solution of boundary value problem for a differential inclusion

On set-valued fixed points, their geometry and solution of boundary value problem for a differential inclusion

On split equality monotone variational inclusion and fixed point problems in reflexive Banach spaces

In this paper, motivated by the works of Akbar and Shahrosvand [Filomat {\bf 32} (2018), no.\ 11, 3917-3932], Ogbuisi and Izuchukwu [Numer. Funct. Anal. Optim. {\bf 41} (2020), no.\ 2, 322-343], and some other related results in the literature, we introduce a Halpern iterative algorithm and employ a Bregman distance approach for approximating a solution of split equality monotone variational inclusion problem and fixed point problem of Bregman relatively nonexpansive mapping in reflexive Banach spaces. Under suitable condition, we state and prove a strong convergence result for approximating a common solution of the aforementioned problems. Furthermore, we give an application of our main result to variational inequality problems and provide some numerical examples to illustrate the convergence behavior of our result. The result presented in this paper extends and complements many related results in literature.

Analyzing knowledge integration in convergence research

A pragmatic concern guides this perspective piece: How might researchers charged with leading convergence research better plan, design, implement, and evaluate the integrative processes and products of their research? We use a self-evaluation approach to assess the integrative processes and products of the first two years of a five-year National Science Foundation Growing Convergence Research project on addressing inland freshwater salinization. To examine the linkages between integration approaches and products, we analyzed the integrative qualities of fifteen research products and the collaborative processes used to generate these products. We found that large, heterogeneous teams with a broad mix of disciplines and professional expertise produced more interdisciplinary research products, but they relied on skilled integration by the leader, more intensive forms of collaboration, and inclusive problem framing. Teams that relied on deliberation by experts and used more consultative or cooperative mechanisms for engagement produced research that was more uni- or multi-disciplinary. We consider the efficacy of the various knowledge integration approaches used in this research and share empirically derived recommendations for designing, implementing, and evaluating convergence research. Our findings and lessons provide researchers at the helm of large-scale convergence and transdisciplinary research projects that address complex socio-environmental problems guidance on: (1) the planning and designing of projects with the explicit goal of knowledge integration; (2) the selection and implementation of appropriate knowledge integration approaches and tools; and (3) how knowledge integration can be conceptualized and evaluated for socio-environmental problems.

Modi ed inertia Halpern method for split null point problem in Banach spaces

Abstract. In this paper, we study split null point problem in reflexive Banach spaces. Using the Bregman technique together with a modified inertial Halpern method, we approximate a solution of split null point problem. Also, we establish a strong convergence result for approximating the solution of the aforementioned problems. It is worth mentioning that the iterative algorithm employ in this study is design in such a way that it does not require prior knowledge of operator norm. We display some numerical examples to illustrate the performance of the proposed iterative method. The result discuss in this paper extends and complements many related results in literature. Mathematics Subject Classification (2010): 47H06, 47H09, 47J05, 47J25. Keywords: Monotone variational inclusion problem, split feasibility problem, firmly nonexpansive-type mapping, fixed point problem, inertial method.

Accelerated iterative splitting methods on Hadamard manifolds

This paper aims to solve the monotone inclusion problem, minimization problem of multiple summands and the generalized Heron problem. We present an innovative approach, the modified normal S-iteration method, designed to approximate common fixed points of nearly nonexpansive sequences and families of operators via the property ( A ) . Some deductions of our results improve some existing results in the literature. To show the applicability of our result, we give application to the inclusion problem via forward–backward splitting method version of our algorithm and minimization problem via Douglas–Rachford splitting method version of our algorithm. To demonstrate the practical utility of the algorithm, we apply it to the generalized Heron problem.

Parallel inertial forward–backward splitting methods for solving variational inequality problems with variational inclusion constraints

The inertial forward–backward splitting algorithm can be considered as a modified form of the forward–backward algorithm for variational inequality problems with monotone and Lipschitz continuous cost mappings. By using parallel and inertial techniques and the forward–backward splitting algorithm, in this paper, we propose a new parallel inertial forward–backward splitting algorithm for solving variational inequality problems, where the constraints are the intersection of common solution sets of a finite family of variational inclusion problems. Then, strong convergence of proposed iteration sequences is showed under standard assumptions imposed on cost mappings in a real Hilbert space. Finally, some numerical experiments demonstrate the reliability and benefits of the proposed algorithm.

Using Special Physical Education Curriculum-Based Measurement to Improve Student Motor Development in Both General and Special Needs Population: Review of Early Research Lasting More than Five Decades

The main goal of this study is to acquaint experts in the field of education with the results of early research, which are related to the problems they face even now when it comes to sensitive groups with special needs. Previous experiences can be a good indicator of different models of action for pedagogues and managers within the modern education system. Inclusive education has become a reality faced by all participants in the process. Effective action models have been adopted in developed countries, primarily Western countries. However, in less developed countries, it is evident that the problem of inclusion is faced later, primarily due to legal regulations and the need for more funds for specific training of all participants. This issue is especially neglected when it comes to inclusion in the physical education of children with various disorders in motor development. Examples from practice in earlier research can be a good guide for overcoming various obstacles that all participants face today, both in special and inclusive physical education. Controversies are still occurring between supporters of the traditional particular education approach versus the modern, inclusive education model. A better familiarity with the issue can contribute to overcoming prejudices, which this overview study of earlier research can contribute.

Enhanced Double Inertial Forward–Backward Splitting Algorithm for Variational Inclusion Problems: Applications in Mathematical Integrated Skill Prediction

Enhanced Double Inertial Forward–Backward Splitting Algorithm for Variational Inclusion Problems: Applications in Mathematical Integrated Skill Prediction

On Hybrid and Non-Hybrid Discrete Fractional Difference Inclusion Problems for the Elastic Beam Equation

On Hybrid and Non-Hybrid Discrete Fractional Difference Inclusion Problems for the Elastic Beam Equation