Inclusion Relations Research Articles

Some integral inequalities for generalized left and right log convex interval-valued functions based upon the pseudo-order relation

Abstract It is a well-known fact that inclusion and pseudo-order relations are two different concepts which are defined on the interval spaces, and we can define different types of convexities with the help of both relations. By means of pseudo-order relation, the present article deals with the new notions of convex functions which are known as left and right log- s s -convex interval-valued functions (IVFs) in the second sense. The main motivation of this study is to present new inequalities for left and right log- s s -convex-IVFs. Therefore, we establish some new Jensen-type, Hermite-Hadamard (HH)-type, and Hermite-Hadamard-Fejér (HH-Fejér)-type inequalities for this kind of IVF, which generalize some known results. To strengthen our main results, we provide nontrivial examples of left and right log- s s -convex IVFs.

BASIC APPLICATIONS OF THE q-DERIVATIVE FOR A GENERAL SUBFAMILY OF ANALYTIC FUNCTIONS SUBORDINATE TO k-JACOBSTHAL NUMBERS

This research paper deals with some radius problems, the basic geometricproperties, general coecient and inclusion relations that are established for functionsin a general subfamily of analytic functions subordinate to k-Jacobsthal numbers.

ON \(A^{\mathcal{I^{K}}}\)–SUMMABILITY

In this paper, we introduce and investigate the concept of \(A^{\mathcal{I^{K}}}\)-summability as an extension of \(A^{\mathcal{I^{*}}}\)-summability which was recently (2021) introduced by O.H.H.~Edely, where \(A=(a_{nk})_{n,k=1}^{\infty}\) is a non-negative regular matrix and \(\mathcal{I}\) and \(\mathcal{K}\) represent two non-trivial admissible ideals in \(\mathbb{N}\). We study some of its fundamental properties as well as a few inclusion relationships with some other known summability methods. We prove that \(A^{\mathcal{K}}\)-summability always implies \(A^{\mathcal{I^{K}}}\)-summability whereas \(A^{\mathcal{I}}\)-summability not necessarily implies \(A^{\mathcal{I^{K}}}\)-summability. Finally, we give a condition namely \(AP(\mathcal{I},\mathcal{K})\) (which is a natural generalization of the condition \(AP\)) under which \(A^{\mathcal{I}}\)-summability implies \(A^{\mathcal{I^{K}}}\)-summability.

Some New Estimates on Coordinates of Generalized Convex Interval-Valued Functions

The theory of convex and nonconvex mapping has a lot of applications in the field of applied mathematics and engineering. The Riemann integrals are the most significant operator of interval theory, which permits the generalization of the classical theory of integrals. This study considers the well-known coordinated interval-valued Hermite–Hadamard-type and associated inequalities. To full fill this mileage, we use the introduced coordinated interval left and right preinvexity (LR-preinvexity) and Riemann integrals for further extension. Moreover, we have introduced some new important classes of interval-valued coordinated LR-preinvexity (preincavity), which are known as lower coordinated preinvex (preincave) and upper preinvex (preincave) interval-valued mappings, by applying some mild restrictions on coordinated preinvex (preincave) interval-valued mappings. By using these definitions, we have acquired many classical and new exceptional cases that can be viewed as applications of the main results. We also present some examples of interval-valued coordinated LR-preinvexity to demonstrate the validity of the inclusion relations proposed in this paper.

Prime ideals of the Burnside ring of a saturated fusion system

In a 1969 article, A. Dress described the prime ideals of the Burnside ring of a finite group G and the inclusion relations between them. One may ask whether similar results exist for the Burnside ring of a saturated fusion system F over a finite p-group S. The present paper answers positively, providing a typology for the prime ideals of A(F) and for those of A(F)(p) as a consequence.

Intracranial vessel wall segmentation with deep learning using a novel tiered loss function incorporating class inclusion.

To develop an automated vessel wall segmentation method on T1-weighted intracranial vessel wall magnetic resonance images, with a focus on modeling the inclusion relation between the inner and outer boundaries of the vesselwall. We propose a novel method that estimates the inner and outer vessel wall boundaries simultaneously, using a network with a single output channel resembling the level-set function height. The network is driven by a unique tiered loss that accounts for data fidelity of the lumen and vessel wall classes and a length regularization to encourage boundary smoothness. Implemented with a 2.5D UNet with a ResNet backbone, the proposed method achieved Dice similarity coefficients (DSC) in 2D of 0.925 ± 0.048, 0.786 ± 0.084, Hausdorff distance (HD) of 0.286 ± 0.436, 0.345 ± 0.419 mm, and mean surface distance (MSD) of 0.083 ± 0.037 and 0.103 ± 0.032 mm for the lumen and vessel wall, respectively, on a test set; compared favorably to a baseline UNet model that achieved DSC 0.924 ± 0.047, 0.794 ± 0.082, HD 0.298 ± 0.477, 0.394 ± 0.431 mm, and MSD 0.087 ± 0.056, 0.119 ± 0.059 mm. Our vessel wall segmentation method achieved substantial improvement in morphological integrity and accuracy compared to benchmark methods. The proposed method provides a systematic approach to model the inclusion morphology and incorporate it into an optimization infrastructure. It can be applied to any application where inclusion exists among a (sub)set of classes to be segmented. Improved feasibility in result morphology promises better support for clinical quantification anddecision.

A Study on Certain Subclasses of Analytic Functions Involving the Jackson q-Difference Operator

We introduce two new subclasses of analytic functions in the open symmetric unit disc using a linear operator associated with the q-binomial theorem. In addition, we discuss inclusion relations and properties preserving integral operators for functions in these classes. This paper generalizes some known results, as well as provides some new ones.

Properties of neighborhood for certain classes associated with complex order and m-q-p-valent functions with higher order

In this paper, by using q-calculus (Jackson’s q-derivative) D_{q,p} we defined new operator D_{lambda ,q,p}^{n}f^{(m)}(z). After that, we used this operator to introduce two new subclasses of multivalent analytic functions with complex order. Also, we obtained coefficients estimates and consequent inclusion relationships involving the N_{j,delta ,m}^{p,q}(f)-neighborhood of these classes

(∆mv , f)-lacunary statistical convergence of order α

In this paper, we define the space Sαθ (∆mv, f) of all (∆mv, f)-lacunary statistical convergent sequences of order α with the help of unbounded modulus function f, lacunary sequence (θ), generalized difference operator ∆ mv and real number α ∈ (0, 1]. We also introduce the space ωαθ (∆mv, f) of all strong (∆mv, f)-lacunary summable sequences of order α. Properties related to these spaces are studied. Inclusion relations between spaces Sαθ (∆mv, f) and ωα θ (∆mv, f) are established under certain conditions.

Boundary region-based variable precision covering rough set models

As an essential way of knowledge representation and knowledge acquisition in uncertainty theory, variable precision rough set (VPRS) has been widely considered by researchers. Firstly, the corresponding CVPRS model via boundary region is investigated based on an existing covering-based rough set model. Its algebraic structures and properties are systematically studied. This model mainly depicts a pair of boundary operators and a pair of approximation operators with a certain threshold from the perspective of single knowledge granularity. And it not only relaxes the complete inclusion relation but also retains the basic properties of the classical rough set. Secondly, an attribute reduction approach is given for a covering-based decision information systemusing the proposed CVPRS model, which keeps the lower or upper approximation unchanged. The different performances of boundary operators and their related three indices in these reduction methods are compared. The results show that boundary operators and distribution functions have outstanding advantages in these applications. Finally, an extraction method of necessity rules and possibility rules corresponding to decision classes are established. The validity and security of the above methods are verified theoretically. Numerical experiments further show that the proposed models and methods have a certain application value.

Nexus between Fiscal Inclusion and Economic Growth of Nepal

This study is aimed to investigate the nexus between financial inclusion and economic growth of Nepal. This study employs descriptive as well as multiple regression model using the data over the period of mid-July 2014 to mid-July 2021 to examine the linkage between financial inclusion and economic growth of Nepal. The empirical results of the study reveal that there is strong association of financial inclusion with economic growth, however, there is no positive and robust impact of financial inclusion on economic growth of Nepal. In contrary, overall analysis of the study shows the strong evidence to support the view that financial inclusion is the backbone of the Nepali economy. This study covers only limited indicators of financial inclusion and limited periods of data which are not enough to evaluate the long-run relations of financial inclusion and growth of Nepal. This study suggests that policies promoting financial deepening and penetration and reforming the financial sectors to bond with the financial inclusion for economic growth of Nepal. In this study, we attempt to assess the significance of financial inclusion in economic growth so that piecemeal efforts can be made to combat Nepal's policy hitches and logjams.

Noise-Tolerant Fuzzy-$\beta$-Covering-Based Multigranulation Rough Sets and Feature Subset Selection

As a novel fuzzy covering, fuzzy <inline-formula><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> covering has attracted considerable attention. However, the traditional fuzzy-<inline-formula><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula>-covering-based rough set and most of its extended models cannot well fit the distribution of samples in real data, which limits their application in classification learning and decision making. First, the upper and lower approximations of these models have no inclusion relation, so they cannot characterize a given objective concept accurately. Moreover, most of these models are hard to resist the influence of noise data, resulting in poor robustness in feature learning. For these reasons, a robust rough set model is set forth by combining fuzzy rough sets, covering-based rough sets, and multigranulation rough sets. To this end, the optimistic and pessimistic lower and upper approximations of a target concept are reconstructed by means of the fuzzy <inline-formula><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> neighborhood related to a family of fuzzy coverings, and a new multigranulation fuzzy rough set model is presented. Furthermore, a fuzzy dependence function is introduced to evaluate the classification ability of a family of fuzzy <inline-formula><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> coverings at different granularity levels. The dimensionality reduction of a given fuzzy covering decision table is carried out from the perspective of maintaining the discrimination power, and a forward algorithm for feature selection is developed by using the optimistic significance of candidate features as heuristic information. Three groups of numerical experiments on 16 different types of datasets demonstrate that the proposed model exhibits good robustness on datasets contaminated with noise and outperforms some state-of-the-art feature learning algorithms in terms of classification accuracy and the size of the selected feature subset.

On Near-Rings with Soft Union Ideals and Applications

In this paper, we define soft union near-ring on a soft set by using soft sets, inclusion relation and union of sets. This new notion functions as a bridge among soft set theory, set theory and near-ring theory. We then derive its basic properties and investigate the relationship between soft intersection near-ring and soft union near-ring. Furthermore, we obtain some analog of classical near-ring theoretic concepts for soft union near-ring and give the applications of soft union near-ring to near-ring theory.

Opinions on Lexical, Phraseological and Motivational Meaning.

The motivation of the word is its specific sign; it is the structural-semantic capacity that allows us to be aware of the interconditioning of the sound form and its meaning by comparing it with other lexical units of the language. The types of motivation of the word meaning are: the lexical motivation which is the result of the expression by the word of the motivational index of the designated object and the structural motivation which is the expression by the word of the classification index of the designated object. Lexical and structural motivations are realized by the internal form of the word (IFW). The IFW components are on the “horizontal” motivational form and the motivational meaning, and on the vertical - the motivational part and the forming part. With reference to words we can speak of lexical meaning and motivational meaning; in SPU (stable polilexical units), however, we identify phraseological meaning, motivational meaning, and lexical meaning. The motivational form of the word (MF) is the segment (or segments of its sound form), determined in terms of its motivation. The motivational meaning of the word is the meaning (or a synthesis of the meanings) of the motivational form. There are different types of relations between the motivational meaning and the lexical meaning of the word: the overlapping relationship; inclusion relationships; intersection relations; and inadvertent relationships. There are various types of motivational indices. The following types of IFW are determined: a) live - when the motivation can be identified by the speaker; b) dead, here the word has lost its motivation in the speaker's perception; c) lexicalized and non-lexicalized; d) metaphorical and non-metaphorical. Examples of the types of motivation mentioned are presented in this article.

Orlicz-lacunary convergent triple sequences and ideal convergence

In the present paper we introduce and study Orlicz lacunary convergent triple sequences over n-normed spaces. We make an effort to present the notion of $g_{3}$-ideal convergence in triple sequence spaces. We examine some topological and algebraic features of new formed sequence spaces. Some inclusion relations are obtained in this paper. Finally, we investigate ideal convergence in these spaces.

On lacunary statistical convergence of sequences in gradual normed linear spaces

In this paper, we introduce and investigate the notion of lacunary statistical convergence of sequences in gradual normed linear spaces. We study some of its basic properties and some inclusion relations. In the end, we introduce the notion of lacunary statistical Cauchy sequences and prove that it is equivalent to the notion of lacunary statistical convergence.

Generalized Fractional Integral Inequalities for p-Convex Fuzzy Interval-Valued Mappings

The fuzzy order relation ≽ and fuzzy inclusion relation ⊇ are two different relations in fuzzy-interval calculus. Due to the importance of p-convexity, in this article we consider the introduced class of nonconvex fuzzy-interval-valued mappings known as p-convex fuzzy-interval-valued mappings (p-convex f-i-v-ms) through fuzzy order relation. With the support of a fuzzy generalized fractional operator, we establish a relationship between p-convex f-i-v-ms and Hermite–Hadamard (ℋ–ℋ) inequalities. Moreover, some related ℋ–ℋ inequalities are also derived by using fuzzy generalized fractional operators. Furthermore, we show that our conclusions cover a broad range of new and well-known inequalities for p-convex f-i-v-ms, as well as their variant forms as special instances. The theory proposed in this research is shown, with practical examples that demonstrate its usefulness. These findings and alternative methodologies may pave the way for future research in fuzzy optimization, modeling, and interval-valued mappings (i-v-m).

Deterministic top-down tree automata with Boolean deterministic look-ahead

We introduce deterministic top-down tree languages with Boolean deterministic look-ahead. We show that the class of deterministic top-down tree languages with deterministic top-down look-ahead and the class of Boolean deterministic tree languages are incomparable under the inclusion relation, and that the union of these two tree language classes is a proper subclass of the class of deterministic top-down tree languages with Boolean deterministic look-ahead, which is a proper subclass of the regular tree languages. We give an inclusion diagram for the above mentioned five tree language classes plus the class of deterministic top-down tree languages. We also show that both the class of deterministic top-down tree languages with deterministic top-down look-ahead and the class of deterministic top-down tree languages with Boolean deterministic look-ahead are closed under binary intersection.

Some Inclusion Relations of Certain Subclasses of Strongly Starlike, Convex and Close-to-Convex Functions Associated with a Pascal Operator

This paper studies some inclusion properties of some new subclasses of analytic functions in the open symmetric unit disc U that are associated with the Pascal operator. Furthermore, the integral-preserving properties in a sector for these subclasses are also investigated.

Generalized vector-valued paranormed sequence spaces defined by a sequence of Orlicz functions

UDC 517.9 In this paper, we introduced a class of generalized vector-valued paranormed sequence space X [ E , A , Δ v m , M , p ] by using a sequence of Orlicz functions M = ( M k ) , a non-negative infinite matrix A = [ a n k ] , generalized difference operator Δ v m and bounded sequence of positive real numbers p k with inf k p k &gt; 0 . Properties related to this space are studied under certain conditions. Some inclusion relations are obtained and a result related to subspace with Orlicz functions satisfying Δ 2 -condition has also been proved.