In this study, we observe the change of roughness degree for the rough Hausdorff convergence of a sequence consisting of the product of a sequence of sets and a sequence of real numbers. Then we prove that the rough Hausdorff convergence is preserved under the operators of addition, union, Cartesian product and convex hull.
{"title":"SOME ROUGH HAUSDORFF LIMIT LAWS FOR SEQUENCES OF SETS","authors":"Ö. Ölmez, Hüseyin Albayrak, S. Aytar","doi":"10.22190/fumi211025043o","DOIUrl":"https://doi.org/10.22190/fumi211025043o","url":null,"abstract":"In this study, we observe the change of roughness degree for the rough Hausdorff convergence of a sequence consisting of the product of a sequence of sets and a sequence of real numbers. Then we prove that the rough Hausdorff convergence is preserved under the operators of addition, union, Cartesian product and convex hull.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82895613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce and study the intuitionistic fuzzy $I$-convergent difference sequence spaces ${I}^{(mu,upsilon)}(T,Delta)$ and ${I^{0}}^{(mu,upsilon)}(T,Delta)$ using by compact operator. Also we introducce a new concept, called closed ball in these spaces. By the helping of these notions, we establish a new topological space and investigate some topological properties in intuitionistic fuzzy $I$-convergent difference sequence spaces ${I}^{(mu,upsilon)}(T,Delta)$ and ${I^{0}}^{(mu,upsilon)}(T,Delta)$ using by compact operator.
{"title":"INTUITIONISTIC FUZZY I-CONVERGENT DIFFERENCE SEQUENCE SPACES DEFINED BY COMPACT OPERATOR","authors":"Esra Kamber","doi":"10.22190/fumi200810033k","DOIUrl":"https://doi.org/10.22190/fumi200810033k","url":null,"abstract":"In this paper, we introduce and study the intuitionistic fuzzy $I$-convergent difference sequence spaces ${I}^{(mu,upsilon)}(T,Delta)$ and ${I^{0}}^{(mu,upsilon)}(T,Delta)$ using by compact operator. Also we introducce a new concept, called closed ball in these spaces. By the helping of these notions, we establish a new topological space and investigate some topological properties in intuitionistic fuzzy $I$-convergent difference sequence spaces ${I}^{(mu,upsilon)}(T,Delta)$ and ${I^{0}}^{(mu,upsilon)}(T,Delta)$ using by compact operator.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80583038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let $E$ be a sublattice of a vector lattice $F$.$left( x_alpha right)subseteq E$ is said to be $ F $-order convergent to a vector $ x $ (in symbols $ x_alpha xrightarrow{Fo} x $), whenever there exists another net $ left(y_alpharight) $ in $F $ with the some index set satisfying $ y_alphadownarrow 0 $ in $F$ and $ vert x_alpha - x vert leq y_alpha $ for all indexes $ alpha $.If $F=E^{simsim}$, this convergence is called $b$-order convergence and we write $ x_alpha xrightarrow{bo} x$. In this manuscript, first we study some properties of $Fo$-convergence nets and we extend same results to the general case. In the second part, we introduce $b$-order continuous operators and we invistegate some properties of this new concept. An operator $T$ between two vector lattices $E$ and $F$ is said to be $b$-order continuous, if $ x_alpha xrightarrow{bo} 0 $ in $E$ implies $ Tx_alpha xrightarrow{bo} 0$ in $F$.
{"title":"A GENERALIZATION OF ORDER CONVERGENCE IN THE VECTOR LATTICES","authors":"Kazem Haghnejad Azar","doi":"10.22190/fumi210417036h","DOIUrl":"https://doi.org/10.22190/fumi210417036h","url":null,"abstract":"Let $E$ be a sublattice of a vector lattice $F$.$left( x_alpha right)subseteq E$ is said to be $ F $-order convergent to a vector $ x $ (in symbols $ x_alpha xrightarrow{Fo} x $), whenever there exists another net $ left(y_alpharight) $ in $F $ with the some index set satisfying $ y_alphadownarrow 0 $ in $F$ and $ vert x_alpha - x vert leq y_alpha $ for all indexes $ alpha $.If $F=E^{simsim}$, this convergence is called $b$-order convergence and we write $ x_alpha xrightarrow{bo} x$. In this manuscript, first we study some properties of $Fo$-convergence nets and we extend same results to the general case. In the second part, we introduce $b$-order continuous operators and we invistegate some properties of this new concept. An operator $T$ between two vector lattices $E$ and $F$ is said to be $b$-order continuous, if $ x_alpha xrightarrow{bo} 0 $ in $E$ implies $ Tx_alpha xrightarrow{bo} 0$ in $F$.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85730827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider an impulsive Sturm-Lioville problem on Sturmian time scales. We investigate the existence and uniqueness of the solution of this problem. We study some spectral properties and self-adjointness of the boundary-value problem. Later, we construct the Green function for this problem. Finally, an eigenfunction expansion is obtained.
{"title":"IMPULSIVE STURM-LIOUVILLE PROBLEMS ON TIME SCALES","authors":"B. Allahverdiev, H. Tuna","doi":"10.22190/fumi220217046a","DOIUrl":"https://doi.org/10.22190/fumi220217046a","url":null,"abstract":"In this paper, we consider an impulsive Sturm-Lioville problem on Sturmian time scales. We investigate the existence and uniqueness of the solution of this problem. We study some spectral properties and self-adjointness of the boundary-value problem. Later, we construct the Green function for this problem. Finally, an eigenfunction expansion is obtained.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77568242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work is intended as an attempt to extend some results of nearly Kählerian Finsler manifolds. We give a condition to generalized $ (a, b, {bf J})- $manifolds to be weakly Landsberg metric. Furthermore, we find the conditions under which a nearly Kähler Finsler manifold has relatively isotropic Landsberg curvature and relatively isotropic mean Landsberg curvature.
{"title":"SOME GEOMETRICAL RESULTS ON NEARLY KÄHLER FINSLER MANIFOLDS","authors":"A. Dehghan Nezhad, Sareh Beizavi, A. Tayebi","doi":"10.22190/fumi210922020d","DOIUrl":"https://doi.org/10.22190/fumi210922020d","url":null,"abstract":"This work is intended as an attempt to extend some results of nearly Kählerian Finsler manifolds. We give a condition to generalized $ (a, b, {bf J})- $manifolds to be weakly Landsberg metric. Furthermore, we find the conditions under which a nearly Kähler Finsler manifold has relatively isotropic Landsberg curvature and relatively isotropic mean Landsberg curvature.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83312752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This research is motivated by similarity of basic equations of $F$-planar mappings of symmetric affine connection space $mathbb A_N$ involved by J. Mike� and N. S. Sinyukov, and which have been studied by Mike��s research group (I. Hinterleitner, P. Pev ska, linebreak J. Str'ansk'a) and almost geodesic mappings (specially almost geodesic mappings of the second type) ofthe space $mathbb A_N$ involved by N. S. Sinyukov and which have been studied by many authors. We used the formulas obtained by N. O. Vesic to obtain invariants for special $F$-planar mappings in this article. These invariants are analogous to invariants of geodesic mappings (the Thomas projective parameter and the Weyl projective tensor).
本研究的动机是由于J. Mike和N. s. Sinyukov所涉及的对称仿射连接空间$mathbb A_N$的平面映射$F$的基本方程的相似性，Mike的研究小组(I. Hinterleitner, P. Pev ska， linebreak J. Str'ansk'a)和N. s. Sinyukov所涉及的空间$mathbb A_N$的几乎测地线映射(特别是第二类几乎测地线映射)已经被许多作者研究过。本文利用N. O. Vesic的公式，得到了特殊平面映射的不变量。这些不变量类似于测地线映射的不变量(Thomas射影参数和Weyl射影张量)。
{"title":"INVARIANTS FOR F-PLANAR MAPPINGS OF SYMMETRIC AFFINE CONNECTION SPACES","authors":"N. Vesić, A. Mihajlović","doi":"10.22190/fumi210921019v","DOIUrl":"https://doi.org/10.22190/fumi210921019v","url":null,"abstract":"This research is motivated by similarity of basic equations of $F$-planar mappings of symmetric affine connection space $mathbb A_N$ involved by J. Mike� and N. S. Sinyukov, and which have been studied by Mike��s research group (I. Hinterleitner, P. Pev ska, linebreak J. Str'ansk'a) and almost geodesic mappings (specially almost geodesic mappings of the second type) ofthe space $mathbb A_N$ involved by N. S. Sinyukov and which have been studied by many authors. We used the formulas obtained by N. O. Vesic to obtain invariants for special $F$-planar mappings in this article. These invariants are analogous to invariants of geodesic mappings (the Thomas projective parameter and the Weyl projective tensor).","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91283585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we have introduced three new types of convergence concepts, namely convergence in p-distance, completely convergence and convergence in metric by considering triple sequences of complex uncertain variable. We have established the interrelationships among these notions and also with the existing ones. In this process, we have proven that the notions of convergence in metric and convergence in almost surely are equivalent in nature. Overall, this study presents a more complete scenario of interconnections between the notions of convergences initiated in different directions.
{"title":"CONVERGENCE OF COMPLEX UNCERTAIN TRIPLE SEQUENCE VIA METRIC OPERATOR, p-DISTANCE AND COMPLETE CONVERGENCE","authors":"Birojit Das","doi":"10.22190/fumi220218026d","DOIUrl":"https://doi.org/10.22190/fumi220218026d","url":null,"abstract":"In this paper, we have introduced three new types of convergence concepts, namely convergence in p-distance, completely convergence and convergence in metric by considering triple sequences of complex uncertain variable. We have established the interrelationships among these notions and also with the existing ones. In this process, we have proven that the notions of convergence in metric and convergence in almost surely are equivalent in nature. Overall, this study presents a more complete scenario of interconnections between the notions of convergences initiated in different directions.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86398597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we prove a new type of stability and hyperstability results forthe following cubic functional equationf (2x + y) + f (2x - y) = 2f (x + y) + 2f (x - y) + 12f(x)in 2-Banach spaces using fixed point approach.
{"title":"A FIXED POINT APPROACH TO STABILITY OF A CUBIC FUNCTIONAL EQUATION IN 2-BANACH SPACES","authors":"K. Y. N. Sayar, A. Bergam","doi":"10.22190/fumi210426017s","DOIUrl":"https://doi.org/10.22190/fumi210426017s","url":null,"abstract":"In this paper, we prove a new type of stability and hyperstability results forthe following cubic functional equationf (2x + y) + f (2x - y) = 2f (x + y) + 2f (x - y) + 12f(x)in 2-Banach spaces using fixed point approach.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73301514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a review of a development of the Drazin inverse for the sum of two matrices has been given. Since this topic is closely related to the problem of finding the Drazin inverse of a 2x2 block matrix, the paper also offers a survey of this subject.
{"title":"ADDITIVE PROPERTIES OF THE DRAZIN INVERSE FOR MATRICES AND BLOCK REPRESENTATIONS: A SURVEY","authors":"Jelena Višnjić","doi":"10.22190/fumi220321029v","DOIUrl":"https://doi.org/10.22190/fumi220321029v","url":null,"abstract":"In this paper, a review of a development of the Drazin inverse for the sum of two matrices has been given. Since this topic is closely related to the problem of finding the Drazin inverse of a 2x2 block matrix, the paper also offers a survey of this subject.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72505077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bahar Doğan Yazıcı, Sıddıka ÖZKALDI KARAKUŞ, M. Tosun
Investigations are very important for non-regular curves in differential geometry. Framed curves have been used recently to study singular curves, and they have many contributions to singularity theory. In this study, framed Tzitzeica curves are introduced with the help of framed curves. In addition, some framed special curves that satisfy the Tzitzeica condition are given. New results have been obtained among the framed curves of these curves.
{"title":"ON FRAMED TZITZEICA CURVES IN EUCLIDEAN SPACE","authors":"Bahar Doğan Yazıcı, Sıddıka ÖZKALDI KARAKUŞ, M. Tosun","doi":"10.22190/fumi211025021d","DOIUrl":"https://doi.org/10.22190/fumi211025021d","url":null,"abstract":"Investigations are very important for non-regular curves in differential geometry. Framed curves have been used recently to study singular curves, and they have many contributions to singularity theory. In this study, framed Tzitzeica curves are introduced with the help of framed curves. In addition, some framed special curves that satisfy the Tzitzeica condition are given. New results have been obtained among the framed curves of these curves.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74470642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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