Parabolic sections were introduced by Huang^[1] to study the parabolic Monge-Ampère equation. In this note, we introduce the generalized parabolic sections $\mathcal{P}$ and define $BMO^q_{\mathcal{P}}$ spaces related to these sections. We then establish the John-Nirenberg type inequality and verify that all $BMO^q_{\mathcal{P}}$ are equivalent for $q \geq 1.$

In this paper, we propose a three point approximating subdivision scheme, with three shape parameters, that unifies three different existing three point approximating schemes. Some sufficient conditions for subdivision curve $C^0$ to $C^3$ continuity and convergence of the scheme for generating tensor product surfaces for certain ranges of parameters by using Laurent polynomial method are discussed. The systems of curve and surface design based on our scheme have been developed successfully in garment CAD especially for clothes modelling.

In this article we introduce the paranormed sequence spaces $( f ,\Lambda, \Delta_m, p)$, $c_0( f ,\Lambda, \Delta_m, p)$ and $l_\infty( f ,\Lambda, \Delta_m, p)$, associated with the multiplier sequence $\Lambda = (\lambda_k)$, defined by a modulus function $ f$. We study their different properties like solidness, symmetricity, completeness etc. and prove some inclusion results.

In this paper we obtain a Liouville type result for a class of quasi-harmonic spheres with rotational symmetry.

We study here $L^1$-convergence of new modified double cosine trigonometric sum and obtain a new necessary and sufficient condition for $L^1$-convergence of double cosine trigonometric series. Also, the results obtained by Moricz^[1],[2] are particular cases of ours.

In this paper we introduce a generalization of Bernstein polynomials based on $q$ calculus. With the help of Bohman-Korovkin type theorem, we obtain $A$−statistical approximation properties of these operators. Also, by using the Modulus of continuity and Lipschitz class, the statistical rate of convergence is established. We also gives the rate of $A$−statistical convergence by means of Peetre’s type $K$−functional. At last, approximation properties of a rth order generalization of these operators is discussed.

In this paper, we will establish the boundedness of the commutator generated by fractional integral operator and $RBMO(\mu)$ function on generalized Morrey space in the non-homogeneous space.

In this paper, we obtain the boundedness of the parabolic singular integral operator $T$ with kernel in $L(\log L)^{1/ \gamma} (S^{n−1})$ on Triebel-Lizorkin spaces. Moreover, we prove the boundedness of a class of Marcinkiewicz integrals $\mu_{\Omega,q}(f)$ from $\|f\|_{\dot{F}_{p}^{0,q}(\mathbf{R}^n)}$ into $L^p(\mathbf{R}^n)$.

We use an iteration scheme to approximate common fixed points of nearly asymptotically nonexpansive mappings. We generalize corresponding theorems of [1] to the case of two nearly asymptotically nonexpansive mappings and those of [9] not only to a larger class of mappings but also with better rate of convergence.

In the paper we give the boundedness estimate of bilinear singular integral operators on Sierpinski gasket inspired from [1].