Uniform Convexity and Convergence of a Sequence of Sets in a Complete Geodesic Space

In this paper, we first introduce two new notions of uniform convexity on a geodesic space, and we prove their properties. Moreover, we reintroduce a concept of the set-convergence in complete geodesic spaces, and we prove a relation between the metric projections and the convergence of a sequence of sets.

Dynamical Behaviors of a Fractional-Order Three Dimensional Prey-Predator Model

In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynamics of our proposed model.

Weighted Norm Inequalities for Multilinear Fourier Multipliers with Mixed Norm

In this paper, weighted norm inequalities for multilinear Fourier multipliers satisfying Sobolev regularity with mixed norm are discussed. Our result can be understood as a generalization of the result by Fujita and Tomita by using the L r -based Sobolev space, 1 < r ≤ 2 with mixed norm.

Numerical Solutions for Laminar Boundary Layer Nanofluid Flow along with a Moving Cylinder with Heat Generation, Thermal Radiation, and Slip Parameter

The investigation of the numerical solution of the laminar boundary layer flow along with a moving cylinder with heat generation, thermal radiation, and surface slip effect is carried out. The fluid mathematical model developed from the Navier-Stokes equations resulted in a system of partial differential equations which were then solved by the multidomain bivariate spectral quasilinearization method (MD-BSQLM). The results show that increasing the velocity slip factor results in an enhanced increase in velocity and temperature profiles. Increasing the heat generation parameter increases temperature profiles; increasing the radiation parameter and the Eckert numbers both increase the temperature profiles. The concentration profiles decrease with increasing radial coordinate. Increasing the Brownian motion and the thermophoresis parameter both destabilizes the concentration profiles. Increasing the Schmidt number reduces temperature profiles. The effect of increasing selected parameters: the velocity slip, Brownian motion, and the radiation parameter on all residual errors show that these errors do not deteriorate. This shows that the MD-BSQLM is very accurate and robust. The method was compared with similar results in the literature and was found to be in excellent agreement.

Fixed Point Theorems for Set-Valued L -Contractions in Branciari Distance Spaces

In this paper, the notion of set-valued L -contractions is introduced, and a new fixed point theorem for such contractions is established. An example to illustrate main theorem is given.

On a p x -Biharmonic Kirchhoff Problem with Navier Boundary Conditions

In this article, we study the existence of solutions for nonlocal p x -biharmonic Kirchhoff-type problem with Navier boundary conditions. By different variational methods, we determine intervals of parameters for which this problem admits at least one nontrivial solution.

Uncertainty Principles for Heisenberg Motion Group

In this article, we will recall the main properties of the Fourier transform on the Heisenberg motion group G = ℍ n ⋊ K , where K = U n and ℍ n = ℂ n × ℝ denote the Heisenberg group. Then, we will present some uncertainty principles associated to this transform as Beurling, Hardy, and Gelfand-Shilov.

Lower Semicontinuity in L 1 of a Class of Functionals Defined on B V with Carathéodory Integrands

We prove lower semicontinuity in L 1 Ω for a class of functionals G : B V Ω ⟶ ℝ of the form G u = ∫ Ω g x , ∇ u d x + ∫ Ω ψ x d D s u where g : Ω × ℝ N ⟶ ℝ , Ω ⊂ ℝ N is open and bounded, g · , p ∈ L 1 Ω for each p , satisfies the linear growth condition lim p ⟶ ∞ g x , p / p = ψ x ∈ C Ω ∩ L ∞ Ω , and is convex in p depending only on p for a.e. x . Here, we recall for u ∈ B V Ω ; the gradient measure D u = ∇ u d x + d D s u x is decomposed into mutually singular measures ∇ u d x and d D s u x . As an example, we use this to prove that ∫ Ω ψ x α 2 x + ∇ u 2 d x + ∫ Ω ψ x d D s u is lower semicontinuous in L 1 Ω for any bounded continuous ψ and any α ∈ L 1 Ω . Under minor addtional assumptions on g , we then have the existence of minimizers of functionals to variational problems of the form G u + u − u 0 L 1 for the given u 0 ∈ L 1 Ω , due to the compactness of B V Ω in L 1 Ω .

Fixed Point Results for an Almost Generalized α -Admissible Z -Contraction in the Setting of Partially Ordered b-Metric Spaces

In this paper, we introduce an almost generalized α -admissible Z -contraction with the help of a simulation function and study fixed point results in the setting of partially ordered b-metric spaces. The presented results generalize and unify several related fixed point results in the existing literature. Finally, we verify our results by using two examples. Moreover, one of our fixed point results is applied to guarantee the existence of a solution of an integral equation.

A Note on Derivative of Sine Series with Square Root

Chaundy and Jolliffe proved that if a n is a nonnegative, nonincreasing real sequence, then series ∑ a n sin n x converges uniformly if and only if n a n ⟶ 0 . The purpose of this paper is to show that if n a n is nonincreasing and n a n ⟶ 0 , then the series f x = ∑ a n sin n x can be differentiated term-by-term on c , d for c , d > 0 . However, f ′ 0 may not exist.