Recently, B.-Y. Chen and O.J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. In this paper, first we study pointwise slant and pointwise pseudo-slant submanifolds of almost contact metric manifolds and then using this notion, we show that there exist a non-trivial class of warped product pointwise pseudo-slant submanifolds of Sasakian manifolds by giving some useful results, including a characterization.

Recently, Radu [Note on the iterates of q and (p, q)-Bernstein operators, Scientific Studies and Research, Series Mathematics and Informatics, 26(2) (2016) 83-94] has investigated the convergence of iterates of q-Bernstein polynomial and (p, q)-Bernstein polynomial with the aids of weakly Picard operators theory. In this article, we establish Kelisky-Rivlin type theorem on the power of the q-Bernstein operators for two dimensional case, (p, q)-Bernstein operators and bivariate (p, q)-Bernstein operators by using contraction principle.

In this paper, we study warped product semi-slant submanifold of type M = N T × f N θ with slant fiber, isometrically immersed in a nearly Trans-Sasakian manifold by finding necessary and sufficient conditions in terms of Weingarten map. A characterization theorem is proved as main result.

In the present paper, we establish two general sharp inequalities for the squared norm of second fundamental form for mixed totally geodesic warped product pseudo-slant submanifolds of the form M ⊥ × f M θ and M θ × f M ⊥ , in a nearly Kenmotsu f -manifold M, which include the squared norm of the warping function and slant angle. Also, equality cases are verified. We proved that some previous results are trivial from our results. Moreover, we generalized the inequality theorems [3] and [26] from our derived results.

In the present paper, we consider non-trivial warped product pseudo slant submanifolds of type M ⊥ × f M θ and M θ × f M ⊥ of Kenmotsu f-manifold M. Firstly, we get some basic properties of these type warped product submanifolds. Then, we prove the general sharp inequalities for mixed totally geodesic warped product pseudo slant submanifolds and also we consider equality cases. Also generalizes some previous inequalities as well.