Asian-European Journal of Mathematics

In this work, we study normal spherical indicatrices (images) in terms of inextensible flows in ${𝔼}^3$. We discuss the geometric properties of the normal spherical indicatrices. Furthermore, we give some new characterizations of curvatures in terms of some partial differential equations in ${𝔼}^3$.

Let $\mathcal{ℬ}(X)$ be the algebra of all bounded linear operators on an infinite-dimensional complex or real Banach space $X$. We prove that a bijective bicontinuous map $\mathrm{\Phi }$ on $\mathcal{ℬ}(X)$ preserves the difference of group invertible operators in both directions if and only if $\mathrm{\Phi }$ is either of the form $\mathrm{\Phi }(T)=\alpha AT{A}^{-1}+\mathrm{\Phi }(0)$ or of the form $\mathrm{\Phi }(T)=\alpha B{T}^{\ast }{B}^{-1}+\mathrm{\Phi }(0)$, where $\alpha$ is a nonzero scalar, $A:X\to X$ and $B:X^{\ast }\to X$ are two bounded invertible linear or conjugate linear operators.

In this paper, we describe a method to determine the structure of the Tarski algebra with a finite set of free generators which is different to that given by Iturrioz and Monteiro in [Les algèbres de Tarski avec un nombre fini de générateurs libres, in Informe Técnico, Vol. 37 (Instituto de Matemática de la Universidad Nacional del Sur, Bahía Blanca, 1994)].

By the use of the celebrated Kato’s inequality, we obtain in this paper some new inequalities for trace class operators on a complex Hilbert space $H.$ Natural applications for functions defined by power series of normal operators are given as well.

In this paper, we give new conditions for existence and uniqueness of best proximity point. Also, we introduce the concept of cyclic contraction and nonexpansive for multivalued map and we give existence and convergence theorems for best proximity point in the complete metric space.

In this paper, we study three-dimensional homogeneous paracontact metric manifolds for which the Reeb vector field of the underlying paracontact structure satisfies a nullity condition. We give example of paraSasakian and non-paraSasakian $(\kappa ,\mu )$-manifolds. Finally, we exhibit explicit example of $\eta$-Einstein manifolds.

In this paper, we investigate the problem of delay-range-dependent robust stability analysis for uncertain neutral systems with interval time-varying delays and nonlinear perturbations. The restriction on the derivative of the discrete interval time-varying delay is removed. By applying the augmented Lyapunov–Krasovskii functional approach, new improved integral inequalities, descriptor model transformation, Leibniz–Newton formula and utilization of zero equation, new delay-range-dependent robust stability criteria are derived in terms of linear matrix inequalities (LMIs) for the considered systems. Numerical examples have shown to illustrate the significant improvement on the conservatism of the delay upper bound over some reported results.

Let $(T_1{𝕄}_1^2,g_1)$ be a unit tangent bundle of Minkowski surface $({𝕄}_1^2,g)$ endowed with the pseudo-Riemannian induced Sasaki metric. In this present paper, we studied the N-Legendre and N-slant curves in which the inner product of its normal vector and Reeb vector is zero and nonzero constant, respectively, in $\left(\right.T_1{𝕄}_1^2,g_1\left)\right.$ and several important characterizations of these curves are given.

In the paper, we consider a finite non-chain commutative ring $R={𝔽}_2+u{𝔽}_2+u^2{𝔽}_2$, where $u^3=u$. We mainly study the construction of quantum codes from cyclic codes over $R$. For this, we obtained self-orthogonal codes over ${𝔽}_2$ as gray images of linear and cyclic codes over $R$, then these codes over ${𝔽}_2$ correspond to a cyclic code over $R$ of odd length $n$ used to determine the parameters of the quantum codes.

The purpose of this paper is to introduce and investigate some $r{g}^{\ast }b$ separation axioms in bigeneralized topological spaces. Using the concepts of regular generalized star b-open sets due to Indirani and Sindhu, the study defines and characterizes ${\mu }_{(m,n)}$-$T_1$, ${\mu }_{(m,n)}$-$T_2$, ${\mu }_{(m,n)}$-regular and ${\mu }_{(m,n)}$-normal spaces.

In this paper, we introduce the concept of generalized $\alpha -\psi$-Suzuki-contractions in the context of quasi $b$-metric-like spaces and we establish some related fixed point theorems. As consequences, we obtain some known fixed point results in the literature. Some concrete examples are also provided illustrating the obtained results.

In this paper, we define a new integral operator in the open unit disk. This operator is considered as a complex Volterra operator. Moreover, we define a new subspace of Hardy space involving the normalized analytic functions. We shall show that the new integral operator is closed in the subspace of normalized functions. Geometric characterizations are established in the sequel. Our display is maintained by the Jack Lemma.

The purpose of this paper is to investigate the counterparts of most of our results on Morita invariants of semirings for semimodules. Among others, we obtain the lattice isomorphisms between the set of all ideals and set of all subsemimodules corresponding to a Morita context of semirings. Also, the preservation of congruences between a semiring and a semimodule corresponding to a Morita context of semirings is established.

The purpose of this paper is to generalize Favard’s inequality for pseudo-integral. We consider two cases for the real semiring $([a,b],\oplus ,\odot )$, when pseudo-operations are defined by a continuous and monotone function and when the pseudo-addition is sup operation and the pseudo-multiplication is generated by a continuous and monotone function.

In this paper, the notions of derivations of types $1$ and $2$ on a BL-algebra $L$ are introduced. We extend the notions of these derivations by introducing the notions of $(\phi ,\psi )$-derivations of types $1$ and $2$, and discuss some related properties. The conditions for $(\phi ,\psi )$-derivations of types $1$ and $2$ to be isotone are provided. The set ${\mathrm{\text{Fix}}}_D(L)$ is defined and conditions for ${\mathrm{\text{Fix}}}_D(L)$ to be a down closed set and an ideal on $L$ are given where $L$ is a Boolean algebra and $D$ is a $(\phi ,\psi )$-derivation of type $1$ on $L$. Finally, the relationship between $\phi$-derivations of types $1$ and $2$ for a Boolean algebra $L$ is determined.