The modulus and phase of the reduced logarithmic derivative of the Hankel function zH^'iz)/Hi'\z) for complex variable z and real order v, are investigated. Special attention is paid to the location of saddle points and their trajectories as v varies.

We present a detailed computation of Ramanujan’s most famous singular modulus, k210, based on the Kronecker Limit Formula.

Let X be a completely regular Hausdorff space, E a Banach lattice, and μ an E-valued countably additive, regular Borel measure on X. Some results about the countable additivity and regularity of the modulus |μ| are proved. Also in special cases, it is proved that L1(μ) = L1(|μ|).

In the present article, we propose the $(p,q)$ variant of genuine Baskakov Durrmeyer operators. We obtain moments and establish some direct results, which include weighted approximation and results in terms of modulus of continuity of second order.

In this paper, using the Steklov function, we introduce the generalized continuity modulus and denethe class of functions Wr;kp;' in the space Lp. For this class, we prove an analog of the estimates in [1]in the space Lp.

In this article we introduce the difference sequence spacesW0[ f ,∆m],W1[ f ,∆m], W∞[ f ,∆m] and S[ f ,∆m], defined by a modulus function f . We obtain a relation between W1[ f ,∆m]∩ l∞[ f ,∆m] and S[ f ,∆m]∩ l∞[ f ,∆m] and prove some inclusion results.

Introduction 1. THIS paper embodies mainly the proof of results announced previously (Hayman (5)). Let f(z) be a non-constant integral function and p u t

Keywords: q-Bernstein–Schurer–Stancu operators q-integers Modulus of smoothness Rate of convergence a b s t r a c t In the present paper, we introduce the Stancu type generalization of the Bernstein–Schurer operators based on q integers. First, we prove the basic convergence of S ða;bÞ n;p ð:; q; xÞ and then obtain the rate of convergence by these operators in terms of the modulus of continuity...