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Facta Universitatis, Series : Mathematics and Informatics
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  This is an Open Access Journal Open Access journal
ISSN (Print) 0352-9665 - ISSN (Online) 2406-047X
Published by U of Niš Homepage  [12 journals]
  • NEW RESULTS ON SEMICLOSED LINEAR RELATIONS

    • Authors: Gherbi Abdellah, Messirdi Bekkai, Messirdi Sanaa
      Pages: 461 - 474
      Abstract: This paper has triple main objectives. The first objective is an analysis of
      some auxiliary results on closedness and boundednes of linear relations. The seconde objective is to provide some new characterization results on semiclosed linear relations. Here it is shown that the class of semiclosed linear relations is invariant under finite and countable sums, products, and limits. We obtain some fundamental new results as well as a Kato Rellich Theorem for semiclosed linear relations and essentially interesting generalizations. The last objective concern semiclosed linear relation with closed range, where we have particularly established new characterizations of closable linear relation.


      PubDate: 2021-10-09
      DOI: 10.22190/FUMI190318034A
       
  • ITERATIVE COMPUTATION FOR SOLVING CONVEX OPTIMIZATION PROBLEMS OVER THE
           SET OF COMMON FIXED POINTS OF QUASI-NONEXPANSIVE AND DEMICONTRACTIVE
           MAPPINGS

    • Authors: Thierno M. M. Sow
      Pages: 475 - 487
      Abstract: In this paper, a new iterative method  for solving  convex minimization  problems over the set of common fixed points of quasi-nonexpansive and demicontractive mappings is constructed. Convergence theorems are also proved in Hilbert spaces without any compactness assumption. As an application, we shall utilize our results to solve quadratic optimization  problems involving bounded linear operator. Our theorems are significant improvements on several important recent results.
      PubDate: 2021-10-09
      DOI: 10.22190/FUMI190815035S
       
  • REGULAR FRACTIONAL DIRAC TYPE SYSTEMS

    • Authors: Bilender P Allahverdiev, Huseyin Tuna
      Pages: 489 - 499
      Abstract: In this paper, we study one dimensional fractional Dirac type systems which includes the right-sided Caputo and the left-sided Riemann-Liouvile fractional derivatives of same order α,α∈(0,1). We investigate the properties of the eigenvalues and the eigenfunctions of this system
      PubDate: 2021-10-09
      DOI: 10.22190/FUMI200318036A
       
  • THE HOMEOMORPHIC PROPERTY OF THE STOCHASTIC FLOW GENERATED BYTHE
           ONE-DEFAULT MODEL IN ONE DIMENSIONAL CASE

    • Authors: Fatima Benziadi
      Pages: 501 - 518
      Abstract: In this paper, we will try to study the same result proved in \cite{10}. So, on the same model and with some assumptions, we will study the property of homeomorphism of the stochastic flow generated by the natural model in a one-dimensional case and with some modifications, based on an important theory of Hiroshi Kunita. This is the main motivation of our research.
      PubDate: 2021-10-09
      DOI: 10.22190/FUMI200403037B
       
  • SOME NEW IDENTITIES FOR THE SECOND COVARIANT DERIVATIVE OF THE CURVATURE
           TENSOR

    • Authors: Miroslav D. Maksimovic, Mića S. Stanković
      Pages: 519 - 528
      Abstract: In this paper we study the second covariant derivative of Riemannian curvature tensor. Some new identities for the second covariant derivative are given. Namely, identities obtained by cyclic sum with respect to three indices are given. In the first case, two curvature tensor indices and one covariant derivative index participate in the cyclic sum, while in the second case one curvature tensor index and two covariant derivative indices participate in the cyclic sum.
      PubDate: 2021-10-09
      DOI: 10.22190/FUMI200930038M
       
  • $\eta$-RICCI SOLITONS AND GRADIENT RICCI SOLITONS ON $\delta$- LORENTZIAN
           TRANS-SASAKIAN MANIFOLDS

    • Authors: Mohd Danish Siddiqi, Mehmet Akif Akyol
      Pages: 529 - 545
      Abstract: The objective of the present research article is to study the $\delta$-Lorentzian trans-Sasakian manifolds conceding the $\eta$-Ricci solitons and gradient Ricci soliton. We shown that a symmetric second order covariant tensor in a $\delta$-Lorentzian trans-Sasakian manifold is a constant multiple of metric tensor. Also, we furnish an example of $\eta$-Ricci soliton on 3-diemsional $\delta$-Lorentzian trans-Sasakian manifold is provide in the region where $\delta$-Lorentzian trans-Sasakian manifold is expanding. Furthermore, we discuss some results based on gradient Ricci solitons on $3$-dimensional $\delta$- Lorentzian trans-Sasakian manifold.
      PubDate: 2021-10-09
      DOI: 10.22190/FUMI201010039S
       
  • $D_a$-HOMOTHETIC DEFORMATION AND RICCI SOLITIONS IN THREE DIMENSIONAL
           QUASI-SASAKIAN MANIFOLDS

    • Authors: Tarak Mandal
      Pages: 547 - 555
      Abstract: In the present paper, we have studied curvature tensors of a quasi-Sasakian manifold with respect to the $D_a$-homothetic deformation. We have deduced the Ricci solition in quasi-Sasakian manifold with respect to the $D_a$-homothetic deformation. We have also proved that the quasi-Sasakian manifold is not $\bar{\xi}$-projectively flat under $D_a$-homothetic deformation. Also we give an example to prove the existance of quasi-Sasakian manifold.
      PubDate: 2021-10-09
      DOI: 10.22190/FUMI201114040M
       
  • LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS IN ARROWHEAD FORM

    • Authors: Ivana Jovović
      Pages: 557 - 573
      Abstract: This paper deals with different approaches for solving linear systems of the first order differential equations with the system matrix in the symmetric arrowhead form.
      Some needed algebraic properties of the symmetric arrowhead matrix are proposed.
      We investigate the form of invariant factors of the arrowhead matrix.
      Also the entries of the adjugate matrix of the characteristic matrix of the arrowhead matrix are considered. Some reductions techniques for linear systems of differential equations with the system matrix in the arrowhead form are presented.
      PubDate: 2021-10-09
      DOI: 10.22190/FUMI201115041J
       
  • WEYL TYPE THEOREMS FOR ALGEBRIACALLY CLASS $p$-$wA(s,t)$ OPERATORS

    • Authors: Mohammad H.M. Rashid, T. Prasad
      Pages: 575 - 584
      Abstract: In this paper, we study Weyl type theorems for $f(T)$, where $T$ is algebraically class $p$-$wA(s, t)$ operator with $0 < p \leq 1$ and $0 < s, t, s + t \leq 1$ and $f$ is an analytic function defined on an open neighborhood of the spectrum of $T$. Also we show that if $A , B^{*} \in B(\mathcal{H}) $ are class $p$-$wA(s, t)$ operators with $0 < p \leq 1$ and $0 < s, t, s + t \leq 1$,then generalized Weyl's theorem , a-Weyl's theorem, property $(w)$, property $(gw)$ and generalized a-Weyl's theorem holds for $f(d_{AB})$ for every $f \in H(\sigma(d_{AB})$, where $ d_{AB}$ denote the generalized derivation $\delta_{AB}:B(\mathcal{H})\rightarrow B(\mathcal{H})$ defined by $\delta_{AB}(X)=AX-XB$ or the elementary operator $\Delta_{AB}:B(\mathcal{H})\rightarrow B(\mathcal{H})$ defined by $\Delta_{AB}(X)=AXB-X$.
      PubDate: 2021-10-09
      DOI: 10.22190/FUMI201214042R
       
  • ON SOME EQUIVALENCE RELATION ON NON-ABELIAN $\CA$-GROUPS

    • Authors: Mohammad A. Iranmanesh, Mohammad Hossein Zareian
      Pages: 585 - 593
      Abstract: A non-abelian group $G$ is called a $\CA$-group ($\CC$-group) if $C_G(x)$ is abelian(cyclic) for all $x\in G\setminus Z(G)$. We say $x\sim y$ if and only if $C_G(x)=C_G(y)$.We denote the equivalence class including $x$ by$[x]_{\sim}$. In this paper, we prove thatif $G$ is a $\CA$-group and $[x]_{\sim}=xZ(G)$, for all $x\in G$, then $2^{r-1}\leq G' \leq 2^{r\choose 2}$.where $\frac { G }{ Z(G) }=2^{r}, 2\leq r$ and characterize all groups whose $[x]_{\sim}=xZ(G)$for all $x\in G$ and $ G \leq 100$. Also, we will show that if $G$ is a $\CC$-group and $[x]_{\sim}=xZ(G)$,for all $x \in G$, then $G\cong C_m\times Q_8$ where $C_m$ is a cyclic group of odd order $m$ andif $G$ is a $\CC$-group and $[x]_{\sim}=x^G$, for all $x\in G\setminus Z(G)$, then $G\cong Q_8$.
      PubDate: 2021-10-09
      DOI: 10.22190/FUMI201225043I
       
  • ON I- CONVERGENCE OF SEQUENCES IN GRADUAL NORMED LINEAR SPACES

    • Authors: Chiranjib Choudhury, Shyamal Debnath
      Pages: 595 - 604
      Abstract: In this paper, we introduce the concepts of $\mathcal{I}$ and $\mathcal{I^{*}}-$convergence of sequences in gradual normed linear spaces. We study some basic properties and implication relations of the newly defined convergence concepts. Also, we introduce the notions of $\mathcal{I}$ and $\mathcal{I^{*}}-$Cauchy sequences in the gradual normed linear space and investigate the relations between them.
      PubDate: 2021-10-09
      DOI: 10.22190/FUMI210108044C
       
  • IDEAL CONVERGENCE OF DOUBLE SEQUENCES OF CLOSED SETS

    • Authors: Ozer Talo, Yurdal Sever
      Pages: 605 - 617
      Abstract: In the present paper, we introduce the concepts of ideal inner and ideal outer limits which always exist even if empty sets for double sequences of closed sets in Pringsheim's sense. Next, we give some formulas for finding ideal inner and outer limits in a metric space. After then, we define Kuratowski ideal convergence of double sequences of closed sets by means of the ideal inner and ideal outer limits of a double sequence of closed sets. Additionally, we give some examples that our result is more general than the results obtained before.
      PubDate: 2021-10-09
      DOI: 10.22190/FUMI210121045T
       
  • ROUGH CONTINUOUS CONVERGENCE OF SEQUENCES OF SETS

    • Authors: Öznur Ölmez, Hüseyin Albayrak, Salih Aytar
      Pages: 619 - 626
      Abstract: In this paper, we define a new type of convergence of sequences of sets by using the continuous convergence (or α-convergence) of the sequence of distance functions. Then we proved in which case it is equivalent to rough Wijsman convergence by considering the different values of the roughness degrees.
      PubDate: 2021-10-09
      DOI: 10.22190/FUMI210202046O
       
  • AN EXAMINATION OF THE CONDITION UNDER WHICH A CONCHOIDAL SURFACE IS A
           BONNET SURFACE IN THE EUCLIDEAN 3-SPACE

    • Authors: Muradiye Çimdiker Aslan, Gülşah Aydın Şekerci
      Pages: 627 - 641
      Abstract: In this study, we examine the condition of the conchoidal surface to be a Bonnet surface in Euclidean 3-space. Especially, we consider the Bonnet conchoidal surfaces which admit an infnite number of isometries. In addition, we study the necessary conditions which have to be fulflled by the surface of revolution with the rotating curve <em>c</em>(<em>t</em>) and its conchoid curve <em>c<sub>d</sub></em>(<em>t</em>) to be the Bonnet surface in Euclidean 3-space.
      PubDate: 2021-10-09
      DOI: 10.22190/FUMI210227047C
       
  • LIFTS OF GOLDEN STRUCTURES ON THE TANGENT BUNDLE

    • Authors: Geeta Verma
      Pages: 643 - 650
      Abstract: The present paper aims to study the complete lift of golden structure on tangent bundles. Integrability conditions for complete lift and third-order tangent bundle are established.


      PubDate: 2021-10-09
      DOI: 10.22190/FUMI210304048V
       
  • GEOMETRIC INEQUALITIES FOR DOUBLY WARPED PRODUCTS POINTWISE BI-SLANT
           SUBMANIFOLDS IN CONFORMAL SASAKIAN SPACE FORM

    • Authors: Mohd Aslam, Mohd Iqbal, Sarvesh Kr. Yadav
      Pages: 651 - 668
      Abstract: In this paper, we have established some geometric inequalities for the squared mean curvature in terms of warping functions of a doubly warped product pointwise bi-slant submanifold of a conformal Sasakian space form with a quarter symmetric metric connection. The equality cases havve also been considered. Moreover, some applications of obtained results are derived.
      PubDate: 2021-10-09
       
  • SOME VECTORS FIELDS ON THE TANGENT BUNDLE WITH A SEMI-SYMMETRIC METRIC
           CONNECTION

    • Authors: Aydin Gezer, Erkan Karakas
      Pages: 669 - 683
      Abstract: Let $M$ is a (pseudo-)Riemannian manifold and $TM$ be its tangent bundle
      with the semi-symmetric metric connection $\overline{\nabla }$. In this
      paper, we examine some special vector fields, such as incompressible vector
      fields, harmonic vector fields, concurrent vector fields, conformal vector
      fields and projective vector fields on $TM$ with respect to the
      semi-symmetric metric connection $\overline{\nabla }$ and obtain some
      properties related to them.
      PubDate: 2021-10-09
      DOI: 10.22190/FUMI210506050G
       
 
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