Jordan Journal of Mathematics and Statistics

Relations between (S^ δ/2 T ^γ S^δ/2 ) ^qδ/γ +δ ≥ S^ δq and T^qγ ≥ (T^γ/2 S^δ T^γ/2 )^qγ /γ +δ and their applications

2024-09-12T11:02:20+03:00

Let B^+(H ) represent the cone comprising all positive invertible operators on a complex separable Hilbert space H . When
T and S belong to B^+(H), it holds true that for any γ ≥ 0, δ ≥ 0, and 0 < q ≤ 1, the following two inequalities are equivalent:

(S^ δ/2 T ^γ S^δ/2 ) ^qδ/γ +δ ≥ S^ δq and T^qγ ≥ (T^γ/2 S^δ T^γ/2 )^qγ /γ +δ

In this article, we will explore the connections between these inequalities and provide some applications of this discovery to operator
class theory. Furthermore, we will provide a positive response to the question posed in [16].

SD-Separability in Topological Spaces

2024-09-12T11:26:02+03:00

Our aim is to introduce a generalization of dense set in topological space, namely SD-dense set, when we used the notion
of somewhere dense closure operator. We provide the characterization of this class of sets, and their implications with dense sets and
with somewhere dense sets, and study their union and intersection properties, moreover we discuss their behavior as subspaces in some
special cases, additionally, we investigate their properties in some particular spaces, and then we prove that SD-dense sets, dense sets,
somewhere dense sets and open sets are equivalent in strongly hyperconnected space, after that we illustrate the image of SD-dense sets
by particular maps; as SD-irresolute map and SD-continuous map. Finally, we define a new axiom of separability, namely SD-separable
space using the notion of SD-dense sets, then we state that SD-separable space is stronger than separable space, and in submaximal
space these notions become equivalent, moreover we study the subspaces and the images of SD-separable spaces.

Optimal Conjugate Gradient with Spline Scheme for Solving Bagley-Torvik Fractional Differential Problems

2024-09-12T11:36:13+03:00

In this work, a non-polynomial spline function is constructed to solve the Bagley-Torvik Fractional Differential Problems
involving derivatives in the Caputo sense. This method transforms the fractional differential equation into a system of linear equations
using a spline scheme. The conjugate gradient method is employed for the iterative solution of the linear system. To validate the accuracy
of the method, numerical examples with known analytical solutions are tested. The numerical experiments demonstrate satisfactory
agreement with the exact solution.

Automorphisms of semidirect products fixing the non-normal subgroup

2024-09-12T11:45:42+03:00

In this paper, we describe the automorphism group of semidirect product of two groups that fixes the non-normal subgroup
of it. We have computed these automorphisms for the non-abelian metacyclic p-group and non-abelian p-groups ( p ≥ 5) of order p4,
where p is a prime.

On the Incomplete ( p, q)−Fibonacci and ( p, q)− Lucas Numbers

2024-09-12T11:48:46+03:00

In this present work, the incomplete ( p, q)−Fibonacci and ( p, q)−Lucas numbers are defined. We examine their recurrence
relations as well as some of their properties. We derive their generating functions.

On Recursive Computation of Moments of Generalized Order Statistics for a Transmuted Pareto Distribution and Characterization

2024-09-12T11:51:17+03:00

In this paper, some relations are obtained for recursive computation of moments of generalized order statistics for a modified
Pareto distribution. The recursive methods are obtained for raw and product moments. We have also obtained the recursive methods tocompute the moments of specific situations which include order statistics and record values. We have also given some characterization results for the modified Pareto distribution.

Some Common Fixed-Point Theorems of Kannan-type Contractions with CLR and EA Property on Fuzzy Metric Spaces

2024-09-12T11:54:15+03:00

This manuscript explores generalized Kannan-type contractions in the framework of fuzzy metric spaces. We prove several
common fixed-point results of these new contractive mappings via common limit in the range and El Moutawakil-Aamri properties.
We provide examples to clarify our results. Our results improvise and generalize a few common fixed-point theorems established by
earlier studies.

Transmuted Fuzzy Entropy: Another Look at Generalized Fuzzy Entropy

2024-09-12T11:57:29+03:00

Generalizing a fuzzy entropy presents a better measure in theory and application. In this article we propose a new concept
of generalizing an entropy on the basis of transmutation distribution function. Three transmuted fuzzy entropies are proposed and
compared with well established generalized fuzzy entropies in the literature.

Computing Nash Optimal Strategies for a Two-Player Positive Game

2024-09-12T11:59:31+03:00

We consider a linear quadratic differential game on an infinite time horizon with two types of an information structure.
The game models are considered in both information structures: the open loop design and feedback design. The Newton solver for
computing the stabilizing solution of the associated Nash-Riccati equations has been established. Moreover, a convergent linearized
iterative method depending on a negative constant is introduced for each information structure. The linearized iteration has a linear
convergence rate, however there are cases where the iteration is faster than Newton’s method. Numerical experiments are implemented to explain the computational advantages of the introduced solvers.

Uncertainty Inequalities for Continuous Laguerre Wavelet Transform

2024-09-12T12:02:05+03:00

This paper deals with the Continuous Laguerre Wavelet Transform CLWT, and we prove several versions of the uncertainty
inequalities. More precisely, we get the analogue of Heisenberg inequality for CLWT. Moreover, dealing with concentration in time
and frequency, we find an L p local type uncertainty principle. Finally, we provide the analogue of Benedicks Amrein Berthier’s type
theorem in the case of CLWT.

Existence results for a coupled system of multi-term Katugampola fractional differential equations with integral conditions

2024-09-12T10:38:00+03:00

This paper investigates a coupled system of nonlinear multi-term Katugampola fractional differential equations. Under
sufficient conditions, it establishes the existence and uniqueness results of the solution by using standard fixed point theorems.
Additionally, the paper includes some illustrative examples to strengthen the presented main results.