IDEAL CONVERGENCE OF DOUBLE SEQUENCES OF CLOSED SETS

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.

LIFTS OF GOLDEN STRUCTURES ON THE TANGENT BUNDLE

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.

ITERATIVE COMPUTATION FOR SOLVING CONVEX OPTIMIZATION PROBLEMS OVER THE SET OF COMMON FIXED POINTS OF QUASI-NONEXPANSIVE AND DEMICONTRACTIVE MAPPINGS

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.

AN EXAMINATION OF THE CONDITION UNDER WHICH A CONCHOIDAL SURFACE IS A BONNET SURFACE IN THE EUCLIDEAN 3-SPACE

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_d</em>(<em>t</em>) to be the Bonnet surface in Euclidean 3-space.

SOME VECTORS FIELDS ON THE TANGENT BUNDLE WITH A SEMI-SYMMETRIC METRIC CONNECTION

Let $M$ is a (pseudo-)Riemannian manifold and $TM$ be its tangent bundlewith the semi-symmetric metric connection $\overline{\nabla }$. In thispaper, we examine some special vector fields, such as incompressible vectorfields, harmonic vector fields, concurrent vector fields, conformal vectorfields and projective vector fields on $TM$ with respect to thesemi-symmetric metric connection $\overline{\nabla }$ and obtain someproperties related to them.

REGULAR FRACTIONAL DIRAC TYPE SYSTEMS

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

ON I- CONVERGENCE OF SEQUENCES IN GRADUAL NORMED LINEAR SPACES

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.

ON SOME EQUIVALENCE RELATION ON NON-ABELIAN $\CA$-GROUPS

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 $G\cong Q_8$.

ROUGH CONTINUOUS CONVERGENCE OF SEQUENCES OF SETS

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.

NEW RESULTS ON SEMICLOSED LINEAR RELATIONS

This paper has triple main objectives. The first objective is an analysis ofsome 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.