Search

In this paper, we present a new class of linear fractional differential operators that are based on classical Gaussian hypergeometric functions. Then, we utilize the new operators and the concept of differential subordination to construct a convex set of analytic functions. Moreover, through an examination of a certain operator, we establish several notable results related to differential subordination. In addition, we derive inclusion relation results by employing Briot–Bouquet differential subordinations. We also introduce a perspective study for developing subordination results using Gaussian hypergeometric functions and provide certain properties for further research in complex dynamical systems. [ABSTRACT FROM AUTHOR]

In this paper, we present a new class of linear fractional differential operators that are based on classical Gaussian hypergeometric functions. Then, we utilize the new operators and the concept of differential subordination to construct a convex set of analytic functions. Moreover, through an examination of a certain operator, we establish several notable results related to differential subordination. In addition, we derive inclusion relation results by employing Briot–Bouquet differential subordinations. We also introduce a perspective study for developing subordination results using Gaussian hypergeometric functions and provide certain properties for further research in complex dynamical systems.

In this paper, we define a differential operator on an open unit disk Δ by using the novel Borel distribution (BD) operator and means of convolution. This operator is adopted to introduce new subclasses of p-valent functions through the principle of differential subordination, and we focus on some interesting inclusion relations of these classes. Additionally, some inclusion relations are derived by using the Bernardi integral operator. Moreover, relevant convolution results are established for a class of analytic functions on Δ , and other results of analytic univalent functions are derived in detail. This study provides a new perspective for developing p-univalent functions with BD and offers valuable understanding for further research in complex analysis. [ABSTRACT FROM AUTHOR]

In this paper, we introduce some new subclasses of analytic functions in the open unit disk U with negative coefficients defined by generalized Alexander integral operator. The aim of the present paper is to determine coefficient inequalities, inclusion relations, neighborhoods, partial sums and integral means properties for functions f belonging to these subclasses. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Henan University of Science & Technology, Natural Science is the property of Editorial Office of Journal of Henan University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We characterize the inclusion relations between weighted classes of entire functions with rapid decreasing growth and study strong growth comparison relations between given weights. In our considerations first we focus on weights defined in terms of the so-called associated weight function where the weight (system) is based on a given sequence. Then the abstract weight function case is reduced to the weight sequence setting by using the so-called associated weight sequence. Finally, we compare weighted entire function spaces defined in terms of so-called dilatation-type and exponential-type weight systems. [ABSTRACT FROM AUTHOR]

In this paper, we define a differential operator on an open unit disk Δ by using the novel Borel distribution (BD) operator and means of convolution. This operator is adopted to introduce new subclasses of p-valent functions through the principle of differential subordination, and we focus on some interesting inclusion relations of these classes. Additionally, some inclusion relations are derived by using the Bernardi integral operator. Moreover, relevant convolution results are established for a class of analytic functions on Δ, and other results of analytic univalent functions are derived in detail. This study provides a new perspective for developing p-univalent functions with BD and offers valuable understanding for further research in complex analysis.

This aim of this paper is to establish the coefficient estimates, distortion theorems, growth theorems and inclusion relations for certain new subclasses of univalent functions in the open unit disc E = {z: |z| < 1}. The results established here, will generalize earlier known results. [ABSTRACT FROM AUTHOR]

In this study, relationships among different bicomplex sequence spaces lp (BC) are examined. Also, using the property of completeness, it is obtained that the spaces lp (BC) are Banach BC-module for 1 ≤ p ≤ ∞ and the spaces lp (BC) are p-Banach BC-module for 0 < p < 1. Moreover, some topological properties of bicomplex sequence spaces such as solidity, seperability etc. are properly investigated. Our proofs and results obtained are well involved and significant. [ABSTRACT FROM AUTHOR]

Let fk(z)=z+∑n=2kanzn{f}_{k}\left(z)=z+{\sum }_{n=2}^{k}{a}_{n}{z}^{n} be the sequence of partial sums of the analytic function f(z)=z+∑n=2∞anznf\left(z)=z+{\sum }_{n=2}^{\infty }{a}_{n}{z}^{n}. In this paper, we determine sharp lower bounds for Re{f(z)/fk(z)}{\rm{Re}}\{f\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}\left(z)\}, Re{fk(z)/f(z)}{\rm{Re}}\{{f}_{k}\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}f\left(z)\}, Re{f′(z)/fk′(z)}{\rm{Re}}\{{f}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}^{^{\prime} }\left(z)\} and Re{fk′(z)/f′(z)}{\rm{Re}}\{{f}_{k}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}^{^{\prime} }\left(z)\}, where f(z)f\left(z) belongs to the subclass Jp,qm(μ,α,β){{\mathcal{J}}}_{p,q}^{m}\left(\mu ,\alpha ,\beta ) of analytic functions, defined by Sălăgean (p,q)\left(p,q)-differential operator. In addition, the inclusion relations involving Nδ(e){N}_{\delta }\left(e) of this generalized function class are considered.

Information measures play a fundamental role in single-valued neutrosophic set (SVNS) theory. The main purpose of this paper is to study the similarity and entropy measures of SVNS with applications in multi-attribute decision making. We proposed the axiomatic definitions of similarity and entropy for single-valued neutrosophic values (SVNVs) with respect to a new kind of inclusion relation between SVNVs. On the basis of Hamming distance, cosine function and cotangent function, three similarity measures and three entropies for SVNVs are constructed. Then, we extended the definitions and construction methods of similarity and entropy for SVNVs to SVNSs by using some aggregation operators. Finally, by using the new similarity and entropy measures we presented a SVNSs based multi-attribute decision making method. It demonstrated that the new information measures presented in this study are applicable and efficient. [ABSTRACT FROM AUTHOR]

It is doubtless that intuitionistic fuzzy set (IFS) theory plays an increasingly important role in solving the problems under uncertain situation. As one of the most critical members in the theory, distance measure is widely used in many aspects. Nevertheless, it is a pity that part of the existing distance measures has some drawbacks in practical significance and accuracy. To make up for their drawbacks and pursue more accuracy and effectiveness, in this paper, we propose a new inclusion relation of IFSs and a new definition called strict distance measure. Based on this new relation, an analysis is given to point out that the common shortcoming of Hamming distance measure and Euclidean distance measure is the mishandling of hesitancy degree. Therefore, the role of hesitancy degree in distance measure is studied deeply and then three strict distance measures are put forward to overcome the above shortcoming. In addition, a novel definition called the characteristic function of distance measure is defined to describe the character of strict distance measure. On this basis, a theorem is presented to illustrate the inevitability of the occurrence of unrecognized result in pattern recognition problems in some special cases. This theorem also shows that the problem cannot be entirely attributed to distance measures. In view of this condition, we provide an appropriate solution. Compared with other existing distance measures in some examples, the superiorities of our improved distance measures are demonstrated to be more effective and more significant. [ABSTRACT FROM AUTHOR]

We characterize the inclusions of weighted classes of entire functions in terms of the defining weights resp. weight systems. First we treat weights defined in terms of a so-called associated weight function where the weight(system) is based on a given sequence. The abstract weight function case is then reduced to the weight sequence setting by using the so-called associated weight sequence. As an application of the main statements we characterize closedness under point-wise multiplication of these classes. [ABSTRACT FROM AUTHOR]

Landcover database often has numerous nonuniform polygons that contain thousands of holes, and even nesting holes. During incremental update, the new changed polygon is used to clip the base state complex polygons, and may intersect a few holes in the latter ones. The traditional update tools, mainly clipping algorithms, must traverse all the holes of complex polygons, which seriously affects the update efficiency. To solve the problem, this paper improves the quadtree spatial index considering the inclusion relations between polygons. In this method, the polygons are divided into two categories: intersecting polygons (intersecting the quadrant axes) and disjointed polygons (disjoint to the quadrant axes). The intersecting polygons are stored on the root nodes on different levels, while the disjointed polygons are stored in the leaf nodes on the index tree. Then, the author introduced the construction of the spatial index and the table of inclusion relations, and explained the operations of the improved quadtree spatial index, namely, insertion, deletion and query. After that, the proposed method was applied to the incremental update of landcover database, and compared with the MX-CIF quadtree index through experiments. The results show that the update efficiency of our method was several times better than that of the contrastive method, and that the efficiency of our method increased with the data volume and complexity. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study the inclusion relations of neutrosophic sets and some applications in multiple attribute decision making. At first, the existing two definitions of inclusion relation (called type-1 and type-2 inclusion relation, respectively) of neutrosophic sets are analyzed, and the deficiencies of type-1 and type-2 inclusion relations are illustrated by examples (in fact, they are actually two extreme cases). Second, a new definition of inclusion relation of neutrosophic sets (call it type-3 inclusion relation) is introduced, and a new method of ranking of neutrosophic sets is given. The effectiveness of the ranking method is presented by some application examples in multiple attribute decision making. Finally, type-3 inclusion relation of neutrosophic sets and related lattice structure are investigated in a systematic way, the definitions of type-3 union and type-3 intersection operations are proposed, and the following important result is proved: all of neutrosophic sets based on a certainty domain constitute a generalized De Morgan algebra (non-distributive lattice) with respect to type-3 union, type-3 intersection and complement operations. From this, the essential difference between neutrosophic set and fuzzy set (and intuitionistic fuzzy set) is clarified theoretically. [ABSTRACT FROM AUTHOR]

In vector landcover database, there are a lot of complex polygons with many holes, even nesting holes. In the incremental updating (i.e., using the change-only information to update the land cover database), a new changed parcel usually has 2-dimensional intersections (e.g., overlap, cover, equal and inside, etc.) with several existing regions, automatic updating operations need to identify the affected objects for the new changes at first. If the existing parcels include complex polygons (i.e., the polygon with holes), it is still needed to determine if there are 2-dimensional intersections between the new changed polygon and each holes of the involved complex polygons. The relation between the complex polygon and its holes has not been presented in the current spatial data indexing methods, only the MBB (Minimum Bounding Box) of the exterior ring of the complex polygon has been stored, the non-involved holes can not be filtered at the first step of spatial access methods. As the refinement geometric operation is costly, therefore the updating process for the complex polygons is very complicated and low efficient using the current spatial data indexing methods. In order to solve this problem, an improved quadtree spatial index method is presented in this paper. In this method, the polygons is divided to two categories according to the relations with the quadrant axes, i.e., disjoint to the axes and intersect with the axes. The intersect polygons are still divided to 5 cases according to the intersection position among the polygons and the different level quadrant axes. The intersection polygons are stored in the different level root nodes in our index tree, and five buckets denoted as XpB, XnB, YpB, YnB, XYB are used to store the polygons intersecting the different level quadrant axes respectively. The polygons disjoint to all quadrant axes are stored in the leaf nodes in this method. The authors developed the spatial index structure with inclusion relations and the algorithms of the corresponding index operations (e.g., insert, delete and query) for the complex polygons. The effectiveness of the improved index is verified by an experiment of land cover data incremental updating. Experimental results show that the proposed index method is significantly more efficient than the traditional quadtree index in terms of spatial query efficiency, and the time efficiency of the incremental updating is increased about 3 times using the proposed index method than that using the traditional quadtree index. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new subclasses of meromorphically p-valent starlike functions. Inclusion relation, integral transforms, and partial sums for each of these classes are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the sharp conditions of the inclusion relations between modulation spaces Ms p,q and Triebel-Lizorkin spaces Fp,r for p ≤ 1, which greatly improve and extend the results for the embedding relations between local Hardy spaces and modulation spaces obtained by Kobayashi, Miyachi and Tomita in [Studia Math. 192 (2009), 79-96]. [ABSTRACT FROM AUTHOR]

In this paper, we establish the sharp conditions for the inclusion relations between Besov spaces B p , q and Wiener amalgam spaces W p , q s . We also obtain the optimal inclusion relations between local hardy spaces h p and Wiener amalgam spaces W p , q s , which completely improve and extend the main results obtained by Cunanana, Kobayashib and Sugimotoa in [3] . In addition, we establish some mild characterizations of inclusion relations between Triebel–Lizorkin and Wiener amalgam spaces, which relates some modern inequalities to classical inequalities. [ABSTRACT FROM AUTHOR]