Distance formulae from Bloch functions to some Möbius invariant function spaces in the unit ball of ℂn such as Qs spaces, little Bloch space ℬ0 and Besov spaces Bp are given.
The multifractal formalism is a formula introduced by Jaffard and Mélot in order to deduce the spectrum of a function from the knowledge of the oscillation exponent of . The spectrum is the Hausdorff dimension of the set of points where has a given value of pointwise regularity. The oscillation exponent is measured by determining to which oscillation spaces (defined in terms of...
For a nonlinear degenerate parabolic equation, how to impose a suitable boundary value condition to ensure the well-posedness of weak solutions is a very important problem. It is well known that the classical Fichera-Oleinik theory has perfectly solved the problem for the linear case, and the optimal boundary value condition matching up with a linear degenerate parabolic equation...
The main object of this paper is to find necessary and sufficient conditions for generalized Bessel functions of first kind to be in the classes and of uniformly spiral-like functions and also give necessary and sufficient conditions for to be in the above classes. Furthermore, we give necessary and sufficient conditions for to be in provided that the function is in the class...
We investigate the boundedness of the strongly singular convolution operators on Herz-type Hardy spaces with variable exponent.
In this paper, we establish and prove some theorems about existence and uniqueness of fixed point for cyclic weakly contraction mappings in dislocated quasi extended b-metric space.
In this article, we discuss a new version of metric fixed point theory. The application of this newly introduced concept is to find some fixed point results where many well-known results in literature cannot be applied. We give some examples to illustrate the given concepts and obtained results.
We study the Banach space () of the harmonic mappings on the open unit disk satisfying the condition where and denote the first complex partial derivatives of . We show that several properties that are valid for the space of analytic functions known as the -Bloch space extend to . In particular, we prove that for the mappings in can be characterized in terms of a Lipschitz...
We investigate a class of fractional Schrödinger-Poisson system via variational methods. By using symmetric mountain pass theorem, we prove the existence of multiple solutions. Moreover, by using dual fountain theorem, we prove the above system has a sequence of negative energy solutions, and the corresponding energy values tend to . These results extend some known results in...
Frame theory is exciting and dynamic with applications to a wide variety of areas in mathematics and engineering. In this paper, we introduce the concept of Continuous ⁎-K-g-frame in Hilbert C⁎-Modules and we give some properties.
In the paper, the author introduces a new class of harmonically convex functions, which is called harmonically -convex functions and establishes some new integral inequalities of the Hermite-Hadamard type for harmonically -convex functions. The properties of the newly introduced class of harmonically convex functions are also investigated. Finally, some applications to special...
The concept of canonical dual -Bessel sequences was recently introduced, a deep study of which is helpful in further developing and enriching the duality theory of -frames. In this paper we pay attention to investigating the structure of the canonical dual -Bessel sequence of a Parseval -frame and some derived properties. We present the exact form of the canonical dual -Bessel...
In this paper, we investigate the distributed optimal control problem for time-fractional differential system involving Schrödinger operator defined on . The time-fractional derivative is considered in the Riemann-Liouville sense. By using the Lax-Milgram lemma, we prove the existence and uniqueness of the solution of this system. For the fractional Dirichlet problem with linear...
It is well known that the modulus of nearly uniform smoothness related with the fixed point property is important in Banach spaces. In this paper, we prove that the modulus of nearly uniform smoothness in Köthe sequence spaces without absolutely continuous norm is . Meanwhile, the formula of the modulus of nearly uniform smoothness in Orlicz sequence spaces equipped with the...
In this paper, we consider the Brezis-Nirenberg problem for the nonlocal fractional elliptic equation ,,,,,, where is fixed, , is a small parameter, and is a bounded smooth domain of . denotes the fractional Laplace operator defined through the spectral decomposition. Under some geometry hypothesis on the domain , we show that all solutions to this problem are least energy...
In this note we establish certain weighted estimates for a class of maximal functions with rough kernels along “polynomial curves“ on . As applications, we obtain the bounds of the above operators on the mixed radial-angular spaces, on the vector-valued mixed radial-angular spaces, and on the vector-valued function spaces. Particularly, the above bounds are independent of the...
In this article, we establish fixed point results for a pair of multivalued mappings satisfying generalized contraction on a sequence in dislocated -quasi metric spaces and Khan type contraction on a sequence in -quasi metric spaces. An example and an application have been discussed. Our results modify and generalize many existing results in literature.
The classical Hölder regularity is restricted to locally bounded functions and takes only positive values. The local regularity covers unbounded functions and negative values. Nevertheless, it has the same apparent regularity in all directions. In the present work, we study a recent notion of directional local regularity introduced by Jaffard. We provide its characterization by a...
In this paper, we establish some functional inequalities for generalized complete elliptic integrals with two parameters, such as estimation of bounds and mean inequalities. Our main results give -analogues to the early results for classical complete elliptic integrals.
In this paper, the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent weak Morrey spaces based on the results of Lebesgue space with variable exponent as the infimum of exponent function equals 1. The corresponding commutators generated by BMO and Lipschitz functions are considered, respectively.
In this paper, a class of predator-prey systems with fear effect is investigated, the integrability conditions of the origin and the positive equilibrium are obtained, and the fact that three limit cycles can be bifurcated from the positive equilibrium is proved, so bistable phenomenon can occur for this system.
In this paper, we introduce the radical th-degree functional equation of the form with a positive integer , discuss its general solutions, and prove new Hyers-Ulam-type stability results for the equation by using Brzdęk’s fixed-point method.
In this paper, we investigate singular Hadamard fractional boundary value problems. The existence and uniqueness of the exact iterative solution are established only by using an iterative algorithm. The iterative sequences have been proved to converge uniformly to the exact solution, and estimation of the approximation error and the convergence rate have also been derived.
In this paper using topological degree we study the existence of nontrivial solutions for a higher order nonlinear fractional boundary value problem involving Riemann-Liouville fractional derivatives. Here, the nonlinearity can be sign-changing and can also depend on the derivatives of unknown functions.