• Volume 92, Issue 2

November 1983,   pages  67-133

• Chapter 7 of Ramanujan’s second notebook

• Bounded starlike functions of complex order

LetF(b, M) (b ≠ 0 complex,M&gt;1/2) denote the class of functionsf(z) =z + Σn=2anzn analytic in U={z:|z|&lt;1} which satisfy for fixedM, f(z)/z ≠ 0 inU and$$\left| {\frac{{b - 1 + \left[ {zf'{{\left( z \right)} \mathord{\left/ {\vphantom {{\left( z \right)} {f\left( z \right)}}} \right. \kern-\nulldelimiterspace} {f\left( z \right)}}} \right]}}{b} - M} \right|&lt; M, z \in U$$. In this note we obtain various representations for functions inF(b, M). We maximize |a3=μa22| over the classF(b, M). Also sharp coefficient bounds are established for functions inF(b, M). We also obtain the sharp radius of starlikeness of the classF(b, M).

• Monotonicity of polymatroids

Unlike matroids, it is observed that there is an upper bound for the numberk such that the polymatroid isk-monotone. We define this upper bound as the monotonicity of polymatroid. We aim to calculate the value of this quantity in terms of the ground rank function of the polymatroid.

• Surface waves in micropolar thermoelasticity

Free surface waves of arbitrary form in a homogeneous and isotropic linear micropolar thermoelastic half-space with stress-free plane boundary are investigated. It is found that all physical quantities associated with the waves are derivable from two scalar functions and that there exist two families of waves in general. One of these is the classical thermoelastic wave modified under the influence of the microelastic field and the other is a new surface wave not encountered in classical elasticity. The waves are not necessarily plane waves and even when these are assumed to propagate in a fixed direction parallel to the boundary, unlike in classical elasticity, the problem is not one of plane strain. Explicit expressions for the displacement vector, microrotation vector and the temperature are obtained and the nature of deformation has been analysed. Several earlier results are deduced as particular cases of the more general results obtained here.

• On the uniform Nörlund summability of Fourier series

A general theorem on uniform Nörlund summability of Fourier series has been derived. Some known results become its special cases.

• Solvability of generalized Hammerstein equations

In this paper we obtain solvability results for generalized Hammerstein equations by using the theory ofk-set contractions.

• # Proceedings – Mathematical Sciences

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