Journal of the Indian Mathematical Society
http://informaticsjournals.com/index.php/jims
The Indian Mathematical Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onward, it is published as its current title 'The Journal of Indian Mathematical Society.<br /><span style="color: blue;">The Journal is Indexed in Scopus with <a href="http://scimagojr.com/journalsearch.php?q=21100259506&tip=sid&clean=0" target="_blank">H Index </a>3. It is also included in UGC Mandate. </span>Informatics Publishing Limited and The Indian Mathematical Societyen-USJournal of the Indian Mathematical Society0019-5839The Bhargava-Adiga Summation and Partitions
http://informaticsjournals.com/index.php/jims/article/view/15836
The Bhargava-Adiga summation rivals the 1ψ1summation of Ramanujan in elegance. This paper is devoted to two applications in the theory of integer partitions leading to partition questions related to Gauss's celebrated three triangle theorem.George E. Andrews
Copyright (c) 2017 Journal of the Indian Mathematical Society
2017-07-012017-07-01843-415116010.18311/jims/2017/15836A New Class of Functions Suggested by the Generalized Basic Hypergeometric Function
http://informaticsjournals.com/index.php/jims/article/view/14969
We introduce an extended generalized basic hypergeometric function rΦs+p in which p tends to infinity together with the summation index. We define the difference operators and obtain infinite order difference equation, for which these new special functions are eigen functions. We derive some properties, as the order zero of this function, differential equation involving a particular hyper-Bessel type operators of infinite order, and contiguous function relations. A transformation formula and an l-analogue of the q-Maclaurin's series are also obtained.Meera H. ChudasamaB. I. Dave
Copyright (c) 2017 Journal of the Indian Mathematical Society
2017-07-012017-07-01843-416118110.18311/jims/2017/14969Convergence and Integrability of Series with Monotone Decreasing Coefficients by Chrestenson - Levy Systems
http://informaticsjournals.com/index.php/jims/article/view/14850
In this paper we consider problems of convergence and integrability of series with monotone decreasing coefficients by Chrestenson - Levy systems. In particular we generalize some results, known for classical Walsh systems. Interest in questions arises due to a rapidly developed greedy algorithm in recent years, where in particular the important role played a representation of functions by series with monotone coefficients.S. A. EpiskoposianT. M. Saghatelyan
Copyright (c) 2017 Journal of the Indian Mathematical Society
2017-07-012017-07-01843-418219010.18311/jims/2017/14850On the Diophantine Equation X<sup>2</sup> + 13<sup>K</sup> = Y<sup>N</sup>
http://informaticsjournals.com/index.php/jims/article/view/15570
The object of this paper is to find all solutions of the dio-phantine equation x<sup>2</sup> + 13<sup>k</sup> = y<sup>n</sup>, in positive integers x, y with n ≥ 3.Abdelkader HamtatDjilali Behloul
Copyright (c) 2017 Journal of the Indian Mathematical Society
2017-07-012017-07-01843-419120010.18311/jims/2017/15570Generalized Sheffer's Classification and Their q-Analague
http://informaticsjournals.com/index.php/jims/article/view/14851
Polynomial sets of type zero and its properties together with various applications were studied in the past. In the Rota theory, the polynomials of Sheer A-type zero are called Sheer sequences. In particular, members of the q-analogue of the Sheer class A-type zero can be called q-Sheer sequences. In the present paper, an attempt is made to discuss q-analogues of generalized Sheer polynomials in two variables and their properties.R. K. JanaS. J. RapeliA. K. Shukla
Copyright (c) 2017 Journal of the Indian Mathematical Society
2017-07-012017-07-01843-420121010.18311/jims/2017/14851On New Classes of Sequence Spaces Inclusion Equations Involving the Sets C<sub>0</sub>, C, l<sub>P</sub>, (1 ≤ P ≤ ∞), W<sub>0</sub> and W<sub>∞</sub>
http://informaticsjournals.com/index.php/jims/article/view/14852
<p>Given any sequence a = (a<sub>n</sub>)<sub>n≥1</sub> of positive real numbers and any set <em>E</em> of complex sequences, we write E<sub>a</sub> for the set of all sequences y = (y<sub>n</sub>)<sub>n≥1</sub> such that y/a = (y<sub>n</sub>/a<sub>n</sub>)<sub>n≥1</sub> ∈ E; in particular, c<sub>a</sub> denotes the set of all sequences y such that y/a converges. Let Φ = {c<sub>0</sub>, c, l<sub>∞</sub>, l<sub>p</sub>, w<sub>0</sub>, w<sub>∞</sub>},(p≥1).. In this paper we apply a result stated in [9] and we deal with the class of (SSIE) of the form F ⊂ E<sub>a</sub>+F'<sub>x</sub> where F∈{c<sub>0,</sub>l<sub>p</sub>, w<sub>0</sub>, w<sub>∞</sub>} and E, F' ∈ Φ. We then obtain the solvability of the corresponding (SSIE) in the particular case when a = (r<sup>n</sup>)<sub>n</sub> and we deal with the case when F = F'. Finally we solve the equation E<sub>r</sub> + (l<sub>p</sub>)<sub>x</sub> = l<sub>p</sub> with E = c<sub>0</sub>, c, s<sub>1</sub>, or l<sub>p</sub> (p≥1). These results extend those stated in [10].</p>Bruno de Malafosse
Copyright (c) 2017 Journal of the Indian Mathematical Society
2017-07-012017-07-01843-421122410.18311/jims/2017/14852Exact Solution of Semi-linear Fuzzy System
http://informaticsjournals.com/index.php/jims/article/view/15569
In this paper we consider a semi-linear dynamical system with fuzzy initial condition. We discuss the results regarding the existence of the solution and obtain the best possible solution for such systems. We give a real life supportive illustration of population model, justify the need for fuzzy setup for the problem, and discuss the solution for it.Purnima K. Pandit
Copyright (c) 2017 Journal of the Indian Mathematical Society
2017-07-012017-07-01843-422523810.18311/jims/2017/15569Existence of Hukuhara Differentiability of Fuzzy-Valued Functions
http://informaticsjournals.com/index.php/jims/article/view/5824
In this paper, we discuss existence of Hukuhara differentiability of fuzzy-valued functions. Several examples are worked out to check that fuzzy-valued functions are one time, two times and n-times H-differentiable. We study the effects of fuzzy modelling on existence of Hukuhara differentiability of fuzzy-valued functions. We discuss existence of gH-differentiability and its comparison with H-differentiability.U. M. PirzadaD. C. Vakaskar
Copyright (c) 2017 Journal of the Indian Mathematical Society
2017-07-012017-07-01843-423925410.18311/jims/2017/5824Homotopy-laplace Decomposition Method to Solve Nonlinear Differential-difference Equations
http://informaticsjournals.com/index.php/jims/article/view/14928
In the recent literature, nonlinear differential equations, integro- differential equations, differential-difference equations and integro-differential-difference equations are studied. Laplace decomposition method and Homotopy analysis method are two powerful decomposition methods employed in the recent literature, nonlinear dierential equations, integro-differential equations, differential-difference equations and integro-differential-difference equations are studied. Laplace decomposition method and Homotopy analysis method are two powerful decomposition methods employed in the literature to solve above nonlinear problems. In the present paper a new method is proposed motivated by the above two methods to solve both nonlinear differential-difference equations and integro-differential-difference equations.R. RangarajanAnanth Kumar S. R.
Copyright (c) 2017 Journal of the Indian Mathematical Society
2017-07-012017-07-01843-425526810.18311/jims/2017/14928Generalization of the Grace Theorem
http://informaticsjournals.com/index.php/jims/article/view/6117
In this paper we extend the theorem of Walsh and some results proved by R. Bakic to a half plane and complement of an open disk.N. A. RatherMohammad Ibrahim
Copyright (c) 2017 Journal of the Indian Mathematical Society
2017-07-012017-07-01843-426927210.18311/jims/2017/6117Soft Set and Soft Group from Classical View Point
http://informaticsjournals.com/index.php/jims/article/view/6123
It is shown that a soft set can be represented as a crisp set of soft elements and a soft group as a ordinary group of soft elements. From this view point it is immediate that soft group share the properties of ordinary group. Also using soft elements the definitions of soft co-sets, soft homomorphism and cyclic soft groups are presented and their properties are studied.S. RayS. Goldar
Copyright (c) 2017 Journal of the Indian Mathematical Society
2017-07-012017-07-01843-427328610.18311/jims/2017/6123On the Dynamics of Composition of Transcendental Entire Functions in Angular Region-II
http://informaticsjournals.com/index.php/jims/article/view/14915
In [14] we showed that for transcendental entire functions f and g, there exist finitely many domains in an angular region, which lie in wandering component of f, wandering component of g and also in wandering component of f ° g and in wandering component of g ° f. Several other related results were discussed in that paper. In this paper we show the existence of such infinite components in angular region, using approximation theory.Garima Tomar
Copyright (c) 2017 Journal of the Indian Mathematical Society
2017-07-012017-07-01843-428729610.18311/jims/2017/14915Bhaskara's Arithmetic Operation of Division by Zero with Application in the Foundation of the Differential Calculus
http://informaticsjournals.com/index.php/jims/article/view/15455
This article is concerned mainly with Bhaskara's arithmetic operation of division by zero. This is the simplest of all for teaching analysis and is the most consistent and philosophical. Some mathematicians have attempted to impugn it, but when I examined their reasonings, I observed that they have done so because they have failed to comprehend the true behavior of zero. In this article I have aimed to clarify and justify Bhaskara's law of impending operations involving zero and furnish hints at the foundations upon which the arithmetic operation of division by zero rests its claims to be preferred to its fashionable rivals, the methods of innitesimals and limits.Okoh Ufuoma
Copyright (c) 2017 Journal of the Indian Mathematical Society
2017-07-012017-07-01843-429732310.18311/jims/2017/15455