Sanjib Kumar Datta

Bio: Sanjib Kumar Datta is an academic researcher from Kalyani Government Engineering College. The author has contributed to research in topics: Entire function & Meromorphic function. The author has an hindex of 6, co-authored 154 publications receiving 238 citations.

Common fixed point theorems under rational contractions for a pair of mappings in bicomplex valued metric spaces

Abstract: In this paper, we have proved some common fixed point theorems for a pair of mappings satisfying certain rational contraction condition in the frame work of bicomplex valued metric space (X...

Measure of growth ratios of composite entire and meromorphic functions with a focus on relative order

Abstract: Some comparative growth properties of composite entire and meromorphic functions on the basis of their relative orders and relative lower orders are discussed in this paper.

Relative Order of Entire Functions in Terms of Their Maximum Terms

Abstract: In the paper we study different properties of relative order of entire functions defined on the basis of their maximum terms. Mathematics Subject Classification: 30D30, 30D35

On the Weak Type of Meromorphic Functions

Abstract: In this paper we introduce the definition of weak type of meromorphic functions and establish its integral representation. We also investigate some growth properties related to the weak type of meromorphic functions. Mathematics Subject Classification: 30D35, 30D30

Theory of Functions

Abstract: THE criticism on the passage quoted from p. 3 of the book by Profs. Harkness and Morley (NATURE, February 23, p. 347) turns on the fact that, in dealing with number divorced from measurement, the authors have used the phrase “an infinity of objects” without an explicit statement of its meaning. I am not sure that I understand the passage in their letter which refers to this point; but it seems to me to imply that the distinction between “finite” and “infinite” is one which does not require definition. This is not the only accepted view. It is not, for instance, the view taken in Herr Dedekind's book, “Was sind und was sollen die Zahlen.” As regards the opening sentences of Chapter xv., the authors have apparently misunderstood the point of my objection. With the usually received definition of convergence of an infinite product, Π(1-αn), if convergent, is different from zero. So far as the passage quoted goes, Π(1-αn) might be zero; and it is therefore not shown to be convergent, if the usual definition of convergence be assumed. As to the passage quoted from p. 232, I must express to the authors my regret for having overlooked the fact that the particular rearrangement, there made use of, has been fully justified in Chapter viii. Whether Log x is or is not, at the beginning of Chapter iv., defined by means of a string and a cone, will be obvious to any one who will read the whole passage (p. 46, line 16, to p. 47, line 9) leading up to the definition.

Unsteady MHD Thin Film Flow of an Oldroyd-B Fluid over an Oscillating Inclined Belt

Abstract: This paper studies the unsteady magnetohydrodynamics (MHD) thin film flow of an incompressible Oldroyd-B fluid over an oscillating inclined belt making a certain angle with the horizontal. The problem is modeled in terms of non-linear partial differential equations with some physical initial and boundary conditions. This problem is solved for the exact analytic solutions using two efficient techniques namely the Optimal Homotopy Asymptotic Method (OHAM) and Homotopy Perturbation Method (HPM). Both of these solutions are presented graphically and compared. This comparison is also shown in tabular form. An excellent agreement is observed. The effects of various physical parameters on velocity have also been studied graphically.

Common fixed point theorems under rational contractions for a pair of mappings in bicomplex valued metric spaces

Abstract: In this paper, we have proved some common fixed point theorems for a pair of mappings satisfying certain rational contraction condition in the frame work of bicomplex valued metric space (X...

Insight into the dynamics of blood conveying alumina nanoparticles subject to Lorentz force, viscous dissipation, thermal radiation, Joule heating, and heat source

Abstract: This analysis studies the impact of the pulsating flow of Al $$_2$$ O $$_3$$ -blood non-Newtonian nanofluid in a channel in the presence of the magnetic field and thermal radiation. Viscous dissipation and Joule heating effects are taken into account. Blood is taken as Oldroyd-B fluid (base fluid) and Al $$_2$$ O $$_3$$ as nanoparticles. The present study is important in engineering and biological models. The walls of channel are assumed to be semi-infinite in length. Assumed that the flow is fully developed and induced by a pressure gradient. Analytical solutions for flow variables are obtained using the perturbation method. The influence of different parameters on temperature and rate of heat transfer have been analysed through graphical results. The results reveal that the temperature of nanofluid accelerates by increasing viscous dissipation and heat source and frequency parameter. Further, the rate of heat transfer enhances with an increase in nanoparticle volume fraction and viscous dissipation.