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In this paper, the existence of positive solutions in terms of different values of two parameters for a system of conformable-type fractional differential equations with the p-Laplacian operator is obtained via Guo-Krasnosel’skii fixed point theorem. [ABSTRACT FROM AUTHOR]

This paper is devoted to characterizing the boundedness of the Riemann-Stieltjes operators from analytic Morrey spaces to Bloch-type spaces. Moreover, the boundedness of the superposition operator and weighted composition operator on analytic Morrey spaces is discussed, respectively. [ABSTRACT FROM AUTHOR]

We define the generalized golden- and product-shaped hypersurfaces in real space forms. A hypersurface M in real space forms Rn+1, Sn+1, and Hn+1 is isoparametric if it has constant principal curvatures. Based on the classification of isoparametric hypersurfaces, we obtain the whole families of the generalized golden- and product-shaped hypersurfaces in real space forms. [ABSTRACT FROM AUTHOR]

We investigate certain recently introduced ODE-determined varying exponent Lp spaces. It turns out that these spaces are finitely representable in a concrete universal varying exponent lp space. Moreover, this can be accomplished in a natural unified fashion. This leads to order-isomorphic isometric embeddings of all of the above Lp spaces to an ultrapower of the above varying exponent lp space. [ABSTRACT FROM AUTHOR]

We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems. [ABSTRACT FROM AUTHOR]

We study the problem of isometric extension on a sphere of the space sn(H). We give an affirmative answer to Tingley's problem in the space sn(H). [ABSTRACT FROM AUTHOR]

We define D-u-anisotropic two-microlocal spaces by decay conditions on anisotropic wavelet coefficients on any D-u-anisotropic wavelet basis of L²(ℝd). We prove that these spaces allow the characterizing of pointwise anisotropic Hölder regularity. We also prove an anisotropic wavelet criterion for anisotropic uniform regularity. We finally prove that both this criterion and anisotropic D-u-two-microlocal spaces are independent of the chosen anisotropic D-u-orthonormal wavelet basis. [ABSTRACT FROM AUTHOR]

Let Tσ be the multilinear Fourier multiplier operator associated with multiplier σ satisfying the Sobolev regularity that sup ...(ℝmn < ∞ for some sκ ∈ (n/2,n] (κ = 1,...,m). The authors prove that if b1...,bm,...,∈ BMO(ℝn and ... then the commutator TσΣb is bounded from LP1(ℝn, w1) x... x LPm(ℝn, wm) to LP(ℝn, ...). Moreover, the authors also prove that if b1,...,bm ∈ VMO(ℝn) and ... ∈...then the commutator TπΣb, is compact operator from LP1 (ℝn, w1) x... x LPm(ℝn,wm) to LP(ℝn,...). [ABSTRACT FROM AUTHOR]

We study the boundedness of Φ-admissible sublinear singular operators on Orlicz-Morrey spaces MΦ, φ(ℝn). These conditions are satisfied by most of the operators in harmonic analysis, such as the Hardy-Littlewood maximal operator and Calderón-Zygmund singular integral operator. [ABSTRACT FROM AUTHOR]

The compact, invertible, Fredholm, and closed range composition operators are characterized. We also make an effort to compute the essential norm of composition operators on the Cesàro function spaces. [ABSTRACT FROM AUTHOR]

This paper is concerned with the functional J defined by J(u) = ∫ΩxΩ W(x, y, ∇u(x), ∇u(y))dx dy, where Ω ⊂ ℝN is a regular open bounded set and W is a real-valued function with variable growth. After discussing the theory of Young measures in variable exponent Sobolev spaces, we study the weak lower semicontinuity and relaxation of J. [ABSTRACT FROM AUTHOR]

The boundedness and compactness of generalized composition operators on Zygmund-Orlicz type spaces and Bloch-Orlicz type spaces are established in this paper. [ABSTRACT FROM AUTHOR]

We study the regularity of the solutions of the surface quasi-geostrophic equation with subcritical exponent 1/2 < α ≤ 1. We prove that if the initial data is small enough in the critical space Ḣ2-2α(ℝ²), then the regularity of the solution is of exponential growth type with respect to time and its Ḣ2-2α(ℝ²) norm decays exponentially fast. It becomes then infinitely differentiable with respect to time and has value in all homogeneous Sobolev spaces Ḣs(ℝ²) for s ≥ 2 - 2α. Moreover, we give some general properties of the global solutions. [ABSTRACT FROM AUTHOR]

The quadratic reciprocal functional equation is introduced. The Ulam stability problem for an ε-quadratic reciprocal mapping f : X → Y between nonzero real numbers is solved. The Găvruța stability for the quadratic reciprocal functional equations is established as well. [ABSTRACT FROM AUTHOR]

We present a semilocal convergence analysis for a uniparametric family of efficient secant-like methods (including the secant and Kurchatovmethod as special cases) in a Ban ach space setting (Ezquerro et al., 2000-2012). Using our idea of recurrent functions and tighter majorizing sequences, we provide convergence results under the same or less computational cost than the ones of Ezquerro et al., (2013, 2010, and 2012) and Hernández et al., (2000, 2005, and 2002) and with the following advantages: weaker sufficient convergence conditions, tighter error estimates on the distances involved, and at least as precise information on the location of the solution. Numerical examples validating our theoretical results are also provided in this study. [ABSTRACT FROM AUTHOR]

The oscillatory hyper-Hilbert transform along curves is of the following form: Hn,α,βf(x) = ∫ 0¹f(x - ⌈(t))e it-β t-1-α dt, where α ≥ 0, β ≥ 0, and ⌈(t) = {tP1, tP2,..., tPn). The study on this operator is motivated by the hyper-Hilbert transform and the strongly singular integráis. The LP bounds for Hn,α,β have been given by Chen et al. (2008 and 2010). In this paper, for some α, β, and p, the boundedness of Hn, α, β on Sobolev spaces LsP(ℝn) and the boundedness of this operator from Ls²(ℝn) to L²(ℝn) are obtained. [ABSTRACT FROM AUTHOR]

By employing the monotone iterative method, this paper not only establishes the existence of the minimal and maximal positive solutions for multipoint fractional boundary value problem on an unbounded domain, but also develops two computable explicit monotone iterative sequences for approximating the two positive solutions. An example is given for the illustration of the main result. [ABSTRACT FROM AUTHOR]

We prove the existence of the PPF dependent fixed point in the Razumikhin class for contractions of rational type in Banach spaces, by using a general class of pairs of functions. Our result has as particular cases a great number of interesting consequences which extend and generalize some results appearing in the literature. [ABSTRACT FROM AUTHOR]

We continue our research on Sobolev spaces on locally compact abelian (LCA) groups motivated by our work on equations with infinitely many derivatives of interest for string theory and cosmology. In this paper, we focus on compact embedding results and we prove an analog for LCA groups of the classical Rellich lemma and of the Rellich-Kondrachov compactness theorem. Furthermore, we introduce Sobolev spaces on subsets of LCA groups and study its main properties, including the existence of compact embeddings into Lℙ-spaces. [ABSTRACT FROM AUTHOR]

The authors prove that Marcinkiewicz integral operator is not only are bounded on Lp, for 1 < P < ∞, but also a bounded map from L¹(Rn) to weak L¹(Rn). Meanwhile, the BMOL-boundedness and (HL¹, L¹)-boundedness are also obtained. Finally, the Lp-boundedness and (L∞, BMOL)-boundedness for the commutator of Marcinkiewicz integral of schrödinger type are established. [ABSTRACT FROM AUTHOR]

We investigate the Hyers-Ulam stability of differentiation operator on Hilbert spaces of entire functions. We give a necessary and sufficient condition in order that the operator has the Hyers-Ulam stability and also show that the best constant of Hyers-Ulam stability exists. [ABSTRACT FROM AUTHOR]

We introduce Triebel-Lizorkin and Besov spaces by Calderóon's reproducing formula on product spaces of homogeneous type.We also obtain smooth atomic and molecular decompositions for these spaces. [ABSTRACT FROM AUTHOR]

Positive solutions of a kind of equations related to the Laplacian and p-Laplacian on a bounded domain in ℝN with ≥ 1 are studied by using variational method. A sufficient condition of the existence of positive solutions is characterized by the eigenvalues of linear and another nonlinear eigenvalue problems. [ABSTRACT FROM AUTHOR]