In this study, some new relations between generalized Fibonacci numbers and matrices are given. The work is designed in three stages: Firstly, it is obtained a relation between generalized Fibonacci numbers and integer powers of the matrices X satisfying the relation X2 = pX +qI, and also, many results are derived from obtained relation. Then, it is established more general relation between generalized Fibonacci numbers and the square matrices X satisfying the condition X2 = VnX - (-q)nI. Finally, some applications and numerical examples related to the obtained results are given.

In this work, a discontinuous singular Dirac system is studied. For this system, a spectral function is constructed. Finally, by using the spectral function, a spectral expansion formula is given

The purpose of the present paper is to obtain some sufficient conditions for analytic functions, whose coefficients are probabilities of the Miller-Ross type-Poisson distribution series, to belong to classes G(λ, δ) and K(λ, δ).

The Jensen and Mercer inequalities are very important inequalities in information theory. The article provides the generalization of Mercer's inequality for convex functions on the line segments. This result contains Mercer's inequality as a particular case. Also, we investigate bounds for Shannon's entropy and give some new applications in zeta function and analysis.

In this paper, we introduce a new class Rkλ (λ ≥ 1, k is any positive real number) of univalent complex functions, which consists of functions f of the form f(z) = z + ∑∞n=2 anzn (|z| < 1) satisfying the subordination condition (1 - λ) f (z)/z + λf′ (z) ≺ 1 + τ2kz2/1 - kτkz - τ2kz2, τk = k - √ k2 + 4/2, and investigate the Fekete-Szegö problem for the coefficients of f ∈ Rk λ which are connected with k-Fibonacci numbers Fk,n = (k - τk)n - τnk/√k2 + 4 (n ∈ N ∪ {0}) . We obtain sharp upper bound for the Fekete-Szegö functional |a3 - μa22| when μ ∈ R. We also generalize our result for μ ∈ C.

The notions of cubic intuitionistic fuzzy set to filters and implicative filters of BE-algebras are introduced. Relations between cubic intuitionistic fuzzy filters with cubic intuitionistic fuzzy implicative filters of BE-algebras are investigated. The homomorphic image and inverse image of cubic intuitionistic fuzzy filters are studied and some related properties are investigated. Also, the product of cubic intuitionistic fuzzy subalgebras (implicative filters) of BE-algebras are investigated.

In this paper, firstly we introduce the concepts of deferred Cesàro summable and deferred statistically convergent function, and secondly we introduce the concepts of deferred almost summable and deferred almost statistically convergent functions. Furthermore, we investigate the relations between these concepts.

Crime committed by civilians and criminals using legal and illegal firearms and conversion of legal firearms into illegal ones has become a common practice around the world. As a result, policies to control civilian gun ownership have been debated in several countries. The issue arose because the linkages between firearm-related mortality, weapon accessibility, and violent crime data can imply diverse options for addressing criminality. In this paper, we have projected a mathematical model in terms of the Caputo fractional derivative to address the issues viz. input of legal guns, crime committed by legal and illegal guns, and strict government policies to monitor the license of legal guns, strict action against violent crime. The boundedness, existence and uniqueness of solutions and the stability of points of equilibrium are examined. It is observed that violent crime increases with the increase of crime committed by illegal guns, crime committed by legal guns and, decreases with the increase of legal guns, the deterrent effect of civilian gun ownership, and action of law against crime. Further, legal guns increase with the increase of the limitation of trade of illegal guns and decrease with the increase of conversion of legal guns into illegal guns and increase of the growth rate of illegal guns. Again, as crime is committed by legal guns also, the policy of illegal gun control does not assure a crime-free society. Weak gun control can lead to a society with less crime. Theoretical aspects are numerically verified in the present work.

In this study, firstly Smarandache ruled surfaces whose base curves are Smarandache curves derived from Frenet vectors of the curve, and whose direction vectors are unit vectors plotting Smarandache curves, are created. Then, the Gaussian and mean curvatures of the obtained ruled surfaces are calculated separately, and the conditions to be developable or minimal for the surfaces are given. Finally, the examples are given for each surface and the graphs of these surfaces are drawn.

On the setting of the orthogonal complement of the weighted Bergman space, we study the problem of when a finite sum of dual Toeplitz products is compact or zero. Our results extend several known results on the unweighted space to the weighted spaces.