Asian-European Journal of Mathematics

In this work, we perform an investigation on the hardness of finding complete decompositions of dihedral groups and show an application of complete decomposition by constructing a Diffie–Hellman-type key exchange protocol.

In this paper, we introduce and study a one-parameter generalization of bihyperbolic Jacobsthal numbers. We give some identities and the generating function for these numbers.

The purpose of this paper is to study the existence and uniqueness of mild solutions to a semilinear Cauchy problem for an abstract nonlocal fractional integrodifferential equation, which has a distinctive nonlinear term. Two sufficient conditions on the existence of mild solutions will be displayed. Continuous dependence of solutions on initial conditions and local $𝜖$-approximate mild solutions will be discussed. An example will be given to elucidate the main results. The results obtained are based upon the method of semigroups, contraction mapping principle, and Krasnoselskii’s fixed point theorem.

In this paper, we introduce a new iterative process for approximation fixed points. We show the stability of our proposed iteration process. We prove some weak and strong convergence theorems for generalized $\alpha$-nonexpansive mappings in the framework of uniformly convex Banach spaces. We also provide an example of a generalized $\alpha$-nonexpansive mapping to show numerically that our iteration is faster than various prominent iteration processes.

In this paper, a combination of the quasilinearization and the Legendre spectral collocation methods is introduced to approximate the solution of the nonlinear functional Volterra integral equations. Throughout this process, the quasilinearization method converts the nonlinear functional Volterra integral equation to a sequence of linear integral equations. Then, in each iteration, the obtained linear integral equation is solved using the Legendre spectral collocation method. After that, a convergence analysis is discussed in detail. Finally, several numerical examples are included to demonstrate the capability and validity of the proposed method.

In this paper, we consider the spectral theory. More precisely, we study the spectral families and their corresponding operators on reflexive Banach spaces. Assume $A$ is a well-bounded operator on reflexive Lebesgue spaces then the operator $A$ is a scalar-type spectral operator. We establish that if a weak spectral family $E(\lambda )$ is concentrated on $[a,b]$ then there exists a linear well-bounded operator $A\in L(X)$ on the reflexive Banach space $X$, such that $〈A(x),y^{*}〉=b〈x,y^{*}〉-{\int }_{[a,b]}〈x,E(\lambda )y^{*}〉d\lambda$ holds for all $x\in X$ and $y^{*}\in X^{*}$. We prove that by assuming $(\mathrm{\Phi },X)$ is a functional calculus on the measurable space $(Z,\mathrm{\Sigma })$, then there are a semi-finite measure space $(\mathrm{\Omega },F,\mu )$ and solitary operator $U:X\to L^p(\mathrm{\Omega },F,\mu )$, and an injective pointwise continuous *-homomorphism $F:M(Z,\mathrm{\Sigma })\to M(\mathrm{\Omega },F)$, such that $\mathrm{\Phi }(f)=U{M}_{Ff}{U}^{-1}$ holds for any operator of the multiplication $M_{Ff}$ that multiplies by function $f$.

In this paper, we introduce certain Kampé de Fériet-like matrix functions and investigate their regions of convergence and recurrence relations satisfied by them. The importance of studying these matrix functions stems from the fact that the derivatives of arbitrary integral order of confluent hypergeometric matrix function and Gauss hypergeometric matrix function with respect to their matrix parameters can be expressed in the form of these Kampé de Fériet-like matrix functions. Integral representations of these matrix functions in a special case are also given.

Suppose $\mathcal{𝒜}$ is an alternative ring containing a non-trivial idempotent and ${\chi }_m$ be a mapping from $\mathcal{𝒜}$ into itself. In this paper, we study the Jordan n-higher derivations on alternative rings and prove that under some mild conditions every multiplicative Jordan n-higher derivations on $\mathcal{𝒜}$ is additive. It is to be noted that the similarity to the notions is only in its written form, but not in its theoretical structures, because the Pierce decomposition used in the results for alternative rings is the generalization of the Pierce decomposition for associative rings.

Let G be a simple, finite, undirected graph with n vertices. The main purpose of this paper introduces the concepts of the minimum covering Gutman Estrada index, the minimum covering Seidel Estrada index, the minimum covering distance Estrada index, the minimum covering Randić Estrada index, the minimum covering Harary Estrada index, and the minimum covering color Estrada index of a graph. First, we compute the new concepts for some of the graphs, such as cocktail party, star, crown, complete and complete bipartite. Moreover, we establish upper and lower bounds for the new concepts.

The main aim of this paper is to introduce the notion of ${\lambda }^2$-statistical convergence in a given uncertainty space by considering sequences of complex uncertain variable. Also, we study the interrelationship between ${\lambda }^2$-statistical convergence with strongly ${\lambda }^2$-summable sequence in the same environment. Further, we extend the study by initiating the notions of ${\lambda }^2$-statistically Cauchy complex uncertain sequence.

In this paper, we explore a subfamily of starlike functions with respect to symmetric points allied with the hyperbolic cosine function. We study Hermitian–Toeplitz determinants of third and fourth orders for the functions belonging to this subfamily. Further, we calculate estimates on the initial successive inverse coefficients as well as logarithmic coefficients and related functionals for such functions. In addition, we also determine bounds on Hankel determinants of third order and symmetric Toeplitz determinants of second and third orders.

Cohen and Taylor [On a certain Lie algebra defined by a finite group, Am. Math. Mon. 114 (2007) 633–639] introduced certain Lie algebras constructed using finite groups called the Plesken Lie algebras. In this paper, we describe the representation of these Plesken Lie algebras, their irreducibility and the Plesken Lie algebra modules.

In this paper, the projective curvature tensor field of a generalized indefinite Sasakian space form is investigated. Some results dealing with projectively semi-symmetric and $\varphi$-projectively semi-symmetric generalized indefinite Sasakian space forms are obtained. Furthermore, biharmonic Legendre Frenet curves are discussed on these manifolds.

In this paper, we study slant curves and Legendre curves in three-dimensional Walker manifolds. We give a classification of these curves and we present a necessary and sufficient condition for a slant curve to admit a proper mean curvature vector field. We close the study by examples.

In this paper, we work out modules with the property that every $z$-closed submodules are essentially embedded in direct summands. This class of modules properly contains the class of CS-modules as well as some of their generalizations. It is shown that the class of modules with former property is closed under direct sums under a certain condition. Taking into account this case, we obtain several results on the inheritance of the latter closure property. Moreover, we consider the behavior of this new property for extensions of modules.

In this paper, we study the enumeration of spanning trees and maximum matchings of the Fibonacci graphs. It is proved that the number of all spanning trees of a Fibonacci graph with $n$ vertices is $(2n-2)$th Fibonacci number. We also obtained a formula for the number of maximum matchings of Fibonacci graphs in terms of Fibonacci numbers.

We investigate the behavior of the lowest geometric constant, ${\lambda }_{a,b}^c(g)$, along the extended Ricci flow such that there exist positive solutions to the following partial differential equation:

The paper proposes multiple new extragradient methods for solving a variational inequality problem involving quasimonotone operators in infinite-dimensional real Hilbert spaces. These methods contain variable stepsize rules that are revised at each iteration and are dependent on prior iterations. These algorithms have the benefit of not requiring prior knowledge of the Lipschitz constant or any line-search approach. Simple conditions are used to demonstrate the algorithm’s convergence. A collection of simple experiments is presented to show the numerical behavior of the algorithms.

In this paper, we introduce and investigate a newly-constructed class of univalent functions in the open disk. For this function class, we obtain upper bounds for the second Hankel determinant $H_2(2)$.

Let $Z(G)$ be the center of a finite non-abelian group $G.$ The non-commuting graph of $G$ is a simple undirected graph with vertex set $G\setminus Z(G),$ and two vertices $u$ and $v$ are adjacent if and only if $uv\ne vu.$ A group $G$ is called a CA-group if the centralizer $C_G(x)$ for every non central element $x$ is abelian. In this paper, we investigate the distance, distance (signless) Laplacian spectra of non-commuting graphs of some CA-groups, and obtain some conditions on them so that the corresponding non-commuting graph is distance, distance (signless) Laplacian integral.