Volume 24, Issue 4

In this paper, we study a class of Riemann–Liouville fractional differential inclusions with fractional boundary conditions. By using standard fixed point theorems, we obtain some new existence results for convex as well as nonconvex multi-valued mappings in an appropriate Banach space. The obtained results are illustrated by examples.

In this paper, we define new classes of meromorphic univalent functions defined in the punctured open unit disc by using a differential operator. Some inclusion results and coefficient inequalities for these classes are studied.

In this paper, we first prove that the normality of a family of k -valued algebroid functions is not equivalent to the normality of the family of the coefficient functions in general. Moreover, by combining the Valiron characteristic function of algebroid functions and the Schottky theorem of holomorphic functions, we investigate the growth relationship between the maximum modulus of an algebroid function and the maximum modulus of its coefficient functions. On this basis, we prove several normality criteria which do not need to restrict the quantity of branch points and contain a very interesting Montel-type normality criterion for entire algebroid function families.

The symmetric and uniform convergence of the series ∑|m|≥1,|n|≥11m⁢n⁢Fm⁢n⁢ei⁢m⁢x,∑|m|≥1,|n|≥11m⁢n⁢Fm⁢n⁢ei⁢n⁢y and ∑|m|≥1,|n|≥11m⁢n⁢Fm⁢n⁢ei⁢(m⁢x+n⁢y)\sum_{|m|\geq 1,|n|\geq 1}\frac{1}{mn}F_{mn}e^{imx},\quad\sum_{|m|\geq 1,|n|% \geq 1}\frac{1}{mn}F_{mn}e^{iny}\quad\text{and}\quad\sum_{|m|\geq 1,|n|\geq 1}% \frac{1}{mn}F_{mn}e^{i(mx+ny)} on [0,2⁢π]{[0,2\pi]} and [0,2⁢π]2{[0,2\pi]^{2}} is established. These series are related to the exponential Fourier series F00+∑|m|≥1Fm⁢0⁢ei⁢m⁢x+∑|n|≥1F0⁢n⁢ei⁢n⁢y+∑|m|≥1,|n|≥1Fm⁢n⁢ei⁢(m⁢x+n⁢y)F_{00}+\sum_{|m|\geq 1}F_{m0}e^{imx}+\sum_{|n|\geq 1}F_{0n}e^{iny}+\sum_{|m|% \geq 1,|n|\geq 1}F_{mn}e^{i(mx+ny)} of a function f which is summable on [0,2⁢π]2{[0,2\pi]^{2}} and 2⁢π{2\pi}-periodic with respect to each variable. The necessary and sufficient conditions on a function f for the integral ∫0x∫0yf⁢(t,τ)⁢𝑑t⁢𝑑τ{\int_{0}^{x}\int_{0}^{y}f(t,\tau)\,dt\,d\tau} to be 2⁢π{2\pi}-periodic with respect to the variables x and y are found.

For a given Laurent polynomial matrix function S , which is positive definite on the unit circle in the complex plane, we consider all possible polynomial spectral factors of S which are not necessarily invertible inside the unit circle.

We consider quasi-monotone functions and discuss various Hardy-type integral inequalities on weighted Lebesgue and grand Lebesgue spaces.

In this paper, a result for double index sequences is established by using a quadratic combination of four operators defined on a Lie algebra of endomorphisms of a vector space. This result is used to give new proofs of some properties of the Bessel and Tricomi functions of two indices. Further, this result is extended for multi-index sequences.

In this paper we prove a stability result for the functional equation 1L⁢∑λ∈KF⁢(x+λ⁢y)=α⁢(y)⁢G⁢(x)+H⁢(y),x,y∈S,\frac{1}{L}\sum_{\lambda\in K}F(x+\lambda y)=\alpha(y)G(x)+H(y),\quad x,y\in S, for the functions F,G,H:S→X{F,G,H\colon S\to X}, α:S→𝕂{\alpha\colon S\to\mathbb{K}}, where (S,+){(S,+)} is an abelian semigroup, K is a finite subgroup of the automorphism group of S , L:=|K|{L:=|K|} and (X,∥⋅∥){(X,\|\cdot\|)} is the Banach space over a field 𝕂∈{ℝ,ℂ}{\mathbb{K}\in\{\mathbb{R},\mathbb{C}\}}.

This paper is concerned with the existence of positive solutions of three classes of nonlinear fractional differential equations using fixed point results in non-zero self-distance spaces. We introduce new concepts of generalized α-weakly (ψ,φ)s{(\psi,\varphi)_{s}}-contractive mappings involving rational terms and then develop fixed point results for weakly α-admissible mappings. Some new examples and counterexamples are given to illustrate the applicability and effectiveness of these results over existing ones. In that way, we extend some previous results. For applications to fractional q -difference boundary value problems, the use of a p -Laplacian operator is suggested.

We consider a model of a dynamic frictional contact between the body and the foundation. In this model the contact is bilateral. The behaviour of the material is described by the elastic-viscoplastic constitutive law with thermal effect. The variational formulation of this model leads to a system of two evolution hemivariational inequalities. The aim of this paper is to prove that this system of inequalities has a unique solution. The proof is based on the Banach fixed point theorem and some results for hemivariational inequalities.

The paper is mainly devoted to the study of the geometry of screen conformal lightlike hypersurfaces of an indefinite cosymplectic manifold. The main result is a characterisation theorem for screen conformal lightlike hypersurfaces of an indefinite cosymplectic space form. The examples of totally geodesic, screen homothetic and screen conformal lightlike hypersurfaces are also given.

Let ψ be an analytic map and ϕ an analytic self-map of the open unit disk 𝔻{\mathbb{D}}. Such maps induce the so-called weighted composition operator Cϕ,ψ:H⁢(𝔻)→H⁢(𝔻){C_{\phi,\psi}:H(\mathbb{D})\to H(\mathbb{D})}, f↦ψ⁢(f∘ϕ){f\mapsto\psi(f\circ\phi)}, where H⁢(𝔻){H(\mathbb{D})} denotes the set of all analytic functions on 𝔻{\mathbb{D}}. We study when such an operator acting between different weighted Bergman spaces has a closed range.

Suppose that Lp,κ⁢(w){L^{p,\kappa}(w)} is a weighted Morrey space in ℝn{\mathbb{R}^{n}}. We establish two-weighted norm inequalities on weighted Morrey spaces for Hilbert and Riesz transforms. Moreover, with the assumption p>n{p>n}, the C-Z singular integral operator is also established for two-weighted norm inequalities on weighted Morrey spaces.