Fej'{e}r  Hadamard  inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r  Hadamard  inequalities for $k$-fractional integrals. We deduce Fej'{e}r  Hadamard-type  inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.

in this paper we consider selberg-type square matrices integrals with focus on kummer-beta types i & ii integrals. for generality of the results for real normed division algebras, the generalized matrix variate kummer-beta types i & ii are defined under the abstract algebra. then selberg-type integrals are calculated under orthogonal transformations.

In this paper, we study the L boundedness of a class of parametric Marcinkiewicz integral operators with rough kernels in L(log L)(Sn−1). Our result in this paper solves an open problem left by the authors of ([6]).

We find necessary density conditions for Marcinkiewicz-Zygmund inequalities and interpolation for spaces of spherical harmonics in S with respect to the L norm. Moreover, we prove that there are no complete interpolation families for p 6= 2.

In this paper, we discuss the boundedness of the fractional type Marcinkiewicz integral operators associated to surfaces, and extend a result given by Chen, Fan and Ying in 2002. They showed that under certain conditions the fractional type Marcinkiewicz integral operators are bounded from the Triebel-Lizorkin spaces Ḟ pq(R ) to L(R). Recently the second author, together with Xue and Yan, great...

We show that every parabolic orbit of a two-degree-of-freedom integrable system admits $$C^{\infty}$$ -smooth Hamiltonian circle action, which is persistent under small perturbations. deduce from this result the structural stability orbits and they are all smoothly equivalent (in non-symplectic sense) to standard model. As corollary, we obtain similar results for cuspidal tori. Our proof based ...

We study the problem of optimal control over process described by a multipoint with oblique derivative for second-order parabolic equation and consider cases internal, starting, boundary control. The performance criterion is specified as sum volume surface integrals. By using principle maximum priori estimates, we establish existence uniqueness solutions boundary-value degeneration. coefficient...