On Solutions of a Parabolic Equation with Nonstandard Growth ConditionRead the full article
Journal of Function Spaces publishes research on all aspects of function spaces, functional analysis, and their employment across other mathematical disciplines.
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Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term
The paper studies the oscillation of a class of nonlinear fractional order difference equations with damping term of the form where , stands for the fractional difference operator in Riemann-Liouville settings and of order , , and is a quotient of odd positive integers and . New oscillation results are established by the help of certain inequalities, features of fractional operators, and the generalized Riccati technique. We verify the theoretical outcomes by presenting two numerical examples.
A Characterization of Central BMO Space via the Commutator of Fractional Hardy Operator
This paper is devoted in characterizing the central BMO space via the commutator of the fractional Hardy operator with rough kernel. Precisely, by a more explicit decomposition of the operator and the kernel function, we will show that if the symbol function belongs to the central BMO space, then the commutator are bounded on Lebesgue space. Conversely, the boundedness of the commutator implies that the symbol function belongs to the central BMO space by exploiting the center symmetry of the Hardy operator deeply.
Monotonicities in Orlicz Spaces Equipped with Mazur-Orlicz -Norm
Some basic properties in Orlicz spaces and Orlicz sequence spaces that are generated by monotone function equipped with the Mazur-Orlicz -norm are studied in this paper. We give some relationships between the modulus and the Mazur-Orlicz -norm. We obtain an interesting result that the norm of an element in line segments is formed by two elements on the unit sphere less than or equal to 1 if and only if that the monotone function is a convex function. The criterion that Orlicz spaces and Orlicz sequence spaces that are generated by monotone function equipped with the Mazur-Orlicz -norm are strictly monotone or lower locally uniform monotone is presented.
Averaging Method for Neutral Stochastic Delay Differential Equations Driven by Fractional Brownian Motion
In this paper, we investigate the stochastic averaging method for neutral stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter . By using the linear operator theory and the pathwise approach, we show that the solutions of neutral stochastic delay differential equations converge to the solutions of the corresponding averaged stochastic delay differential equations. At last, an example is provided to illustrate the applications of the proposed results.
On Best Proximity Point Results for Some Type of Mappings
In this paper, we give new conditions for existence and uniqueness of a best proximity point for Geraghty- and Caristi-type mappings. The presented results are most valuable generalizations of the Geraghty and Caristi fixed point theorems.
The Compact Finite Difference Method of Two-Dimensional Cattaneo Model
In this paper, we propose and analyze the compact finite difference scheme of the two-dimensional Cattaneo model. The stability and convergence of the scheme are proved by the energy method, the convergence orders are in time and in space. We also use the variables separation method to find the true solution of the problem. On this basis, the validity and accuracy of the scheme are verified by numerical experiments.