• Abstract

In this paper, we consider the generalized translations associated with the Dunkland the Jacobi-Dunkl differential-difference operators on the real line which provide thestructure of signed hrpergroups on R. Especially, we study the representation of the generalizedtranslations of the product of two functions for these signed hypergroups.

• Abstract

In this paper, the authors prove that the multilinear fractional integral operator$T_{\Omega,\alpha}^{A1,A2}$ and the relevant maximal operator $M_{\Omega,\alpha}^{A1,A2}$ W,a with rough kernel are both bounded from$L^p$ $(1 < p < \infty)$ to $L^q$ and from $L^p$ to $L^{n/(n−a),\infty$ with power weight, respectively, where$$T_{\Omega,\alpha}^{A1,A2}( f )(x) =\int_{R^n}\frac{{R_{m_1}}(A_1;x,y){R_{m_2}}(A_2;x,y)}{|x-y|^{n-\alpha+m_1+m_2_2}}\Omega(x-y)f(y)dy$$and$$M_{\Omega,\alpha}^{A1,A2}(f)(x)= \sup_{r & gt 0}\frac{1}{r^n−\alpha +m_1+m_2−2}\int_{|x−y| \< r}\prod_{i=1}^{2}{R_{m_i}}(A_i;x,y)\Omega(x-y)f(y)dy$$ and $0 < \alpha < n$, $\Omega \in L^s(S^n−1)$ $(s \geq 1)$ is a homogeneous function of degree zero in $R^n$, $A_i$ is a function defined on $R^n$ and $R_{m_i} (A_i;x,y)$ denotes the $m_i$−th remainder of Taylor seriesof $A_i$ at $x$ about $y$. More precisely, $R_{m_i}$ (A_i;x,y) = A_i(x)− \sum_{|\gamma|< m_i}\frac{1}{\gamma!}D^\gammaA_i(y)(x−y)^r,$ where$D^\gamma (Ai) \in BMO(R^n)$ for $|\gamma | = m_i−1(m_i > 1)$, $i = 1,2$.

• Abstract

A new generalization of Stancu polynomials based on the q-integers and anonnegative integer $s $ is firstly introduced in this paper. Moreover, the shape-preserving andconvergence properties of these polynomials are also investigated.

• Abstract

In this paper we extend Enestrom -Kakeya theorem to a large class of polynomialswith complex coefficients by putting less restrictions on the coefficients. Our resultsgeneralise and extend many known results in this direction.

• Abstract

In this paper we develop the Banach contraction principle and Kannan fixedpoint theorem on generalized conemetric spaces. We prove a version of Suzuki and Kannantype generalizations of fixed point theorems in generalized cone metric spaces.

• Abstract

This paper concerns with the fractional integrals, which are also known as theRiesz potentials. A characterization for the boundedness of the fractional integral operatorson generalized Morrey spaces will be presented. Our results can be viewed as a refinementof Nakai’s[7].

• Abstract

Iterated function systems (IFS) were introduced by Hutchinson in 1981 as anatural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahuand A. Chakraborty introduced K-Iterated Function System using Kannan mapping whichwould cover a larger range of mappings. In this paper, following Hutchinson, D. R. Sahuand A. Chakraborty, we present some new iterated function systems by using the so-calledgeneralized contractive mappings, which will also cover a large range of mappings. Ourpurpose is to prove the existence and uniqueness of attractors for such class of iteratedfunction systems by virtue of a Banach-like fixed point theorem concerning generalizedcontractive mappings.

• Abstract

In this paper, some weighted estimates for the multivariate Hausdorff operatorsare obtained. It is proved that themultivariateHausdorff operators are bounded on L^p spaceswith power weights, which is based on the boundedness of multivariate Hausdorff operatorson Herz spaces, and are bounded on weighted L^p spaces with the weights satisfying thehomogeneity of degree zero.

• Abstract

In this paper, we will discuss the behavior of a class of rough fractional integraloperators on variable exponent Lebesgue spaces,and establish their boundedness from$L^{p_1}(\cdot)(R^n)$ to $L^{p_2}(\cdot)(R^n)$.

• Abstract

In this paper, we consider the following subadditive set-valued map $F : X \to P_0(Y)$:$$F\Big(\sum_{i=1}^r x_i + \sum_{j=1}^s x_{r+j} \Big)\subseteq rF\Big(\frac{\sum_{i=1}^r x_i}{r}\Big)+sF\Big(\frac{\sum_{j=1}^s x_{r+j}{s}\Big),\forall x_i\in X, i=1,2,\cdots, r+s,$$where $r$ and $s$ are two natural numbers. And we discuss the existence and unique problemof additive selection maps for the above set-valued map.