The Journal of the Indian Mathematical Society

A Weighted Hardy-Type Inequality in Time Scale

Sonali Sahu — 2024-07-01

In this article, we establish some new dynamic inequalities for convex decreasing functions on time scale. A refinement of Hardy type inequality with exponential weight is obtained on time scale. As an application, some higher integrability theorems are derived.

The Outer Regularity of the Hewitt-Stromberg Measures in a Metric Space and Applications

Zied Douzi — 2024-07-01

The aim of this paper is to show that if the Hewitt-Stromberg pre-measures are finite, then these pre-measures have a kind of outer regularity in a general metric space X. We also give some conditions on the Hewitt-Stromberg pre-measures such that the Hewitt-Stromberg measures are regular on a complete separable metric space X. In addition, if the measure µ satisfies the doubling condition then the Hewitt-Stromberg pre-measure and measure are both zero or nonzero. As an application, we obtain new sufficient conditions for the valid refined multifractal formalism which is based on the Hewitt-Stromberg measures.

Some Problems Related to Totally Positive Functions and Totally Bounded Functions

B. Thalmi — 2024-07-01

In this paper, we show that a real valued function f defined on any closed bounded interval [a, b] is totally positive if it is Taylor positive. Also, it is shown that the function f is totally bounded if it is Taylor bounded.

Categorical Construction of Minimal Model of Lie Algebra

M. Routaray — 2024-07-01

Under a reasonable assumption, the minimal model of a 1-connected differential graded Lie algebra can be expressed as the Adams cocompletion of the differential graded Lie algebra with respect to a given set of differential graded Lie algebra maps.

On a Class of (p,q)-Laplacian Nonlinear System Involving Nonlocal Operators

Saleh Shakeri — 2024-07-01

In this paper, using sub-super solution argument, we prove some existence results on positive solutions for a class of nonlocal elliptic systems in bounded domains. We employ the method of sub-super solutions to establish our results.

Factorization of a Formal Power Series with Constant Term Certain Power of a Prime

Mriganka S. Dutta — 2024-07-01

This article explores formal power series with integer coefficients, specifically those of a particular form. The primary focus lies in the factorization and irreducibility criteria for these power series. An algorithm is presented for the factorization of power series with a constant term that is the cube of a prime, subject to specific conditions. Furthermore, we establish an irreducibility criterion applicable to power series with a constant term represented by the cube of a prime, as well as higher powers of a prime. The results not only contribute to the understanding of these specialized power series but also provide a practical algorithm for their factorization under certain constraints. The findings have broader implications for the study of power series with integer coefficients, offering insights into their structural properties and mathematical significance.

Uniqueness of Linear Differential Polynomial and Shift of a Meromorphic Function

Renukadevi S. Dyavanal — 2024-07-01

In this paper, we study the uniqueness problems of entire and meromorphic functions concerning their shift and linear differential polynomial.

Continuous Controlled Generalized Fusion Frames in Hilbert Spaces

Prasenjit Ghosh — 2024-07-01

We introduce the notion of continuous controlled g-fusion frame in Hilbert space which is a generalization of discrete controlled g-fusion frame. Some characterizations of continuous controlled g-fusion frame have been presented.We define the frame operator and multiplier of continuous controlled g-fusion Bessel families in Hilbert spaces. Continuous resolution of the identity operator on a Hilbert space using the theory of continuous controlled g-fusion frame is being considered. Finally, we discuss perturbation results of continuous controlled g-fusion frame.

On a Posteriori Error Bound for Weak Galerkin Finite Element Method for Semilinear Parabolic Problems

P. V. Anjali — 2024-07-01

This article presents a posteriori error analysis for the weak Galerkin finite element method based on the backward Euler approximation for semilinear parabolic problems in a bounded convex polygonal domain in R² . An optimal order a posteriori error bound is obtained with respect to the L² -norm in time and in the energy norm in space for the fully discrete backward Euler weak Galerkin finite element method for semilinear parabolic problems. We have exploited the elliptic reconstruction technique combined with the energy arguments to derive error bound. The source term is assumed to satisfy the Lipschitz condition. Numerical results are reported to validate the asymptotic behaviour of the derived error estimators.

Extended Chebyshev Wavelet of First Kind and its Applications in Approximation of a Function Belonging to Holder's Class and Solution of Fredholm Integral Equation of Second Kind

Shyam Lal — 2024-07-01

In this paper, six approximations of solution functions of the Fredholm integral equation in H¨older’s class by first kind extended Chebyshev wavelet expansion in the interval [0, 1) have been estimated. The solutions of the Fredholm integral equation of the second kind by extended Chebyshev wavelets of the first kind have been obtained. The solutions obtained by an extended Chebyshev wavelet of the first kind are approximately the same as their exact solutions. This is a significant achievement of this research paper in wavelet analysis.

On Some Norland I-Convergent Double Sequence Spaces of M-Orlicz Functions

Nazneen Khan — 2024-07-01

Present work is an investigation of some new I− convergent double sequence spaces over an admissible ideal of N² defined by a M−Orlicz function as a domaim of N¨orlund mean. Further, we study some algebraic, topological properties and inclusion relations on these spaces.

Results for Coupled Fixed Point in Partial Metric Spaces via Contractive Type Condition Involving Rational Term

G. S. Saluja — 2024-07-01

The purpose of this paper is to establish a coupled fixed point theorem for contractive type condition involving rational term in the setting of partial metric spaces using control function. Furthermore, we provide some consequences of the established result. We demonstrate that the coupled fixed point problem of the aforementioned result is well-posed. Our results extend and generalize several previously published results from the existing literature.

Existence of Three Solutions for a Class of Nonlocal Neumann Problem

Amar Pal Verma — 2024-07-01

We study the existence of three weak solutions for the class of nonlinear fractional elliptic problem.

Skew Cyclic Codes over a Finite Ring : A Note on a Result of Mohammadi et al.

Swati Bhardwaj — 2024-07-01

In this note we correct an error made by Mohammadi et al. in their paper entitled “On Skew Cyclic Codes Over A Finite Ring”.

On the Study of Ψ-Caputo Fractional Neutral Functional Differential Equation

M. S. Shabna — 2024-07-01

This paper is devoted in the study of the existence, uniqueness and stabilities of solutions for Ψ-Caputo fractional neutral functional differential equation.

Some Permutation Trinomials over Finite Fields F₂^2m

P. L. Sharma — 2024-07-01

Permutation trinomials play an important role in various fields such as finite geometry, combinatorial design and cryptography. Here, we present the constructions of some new classes of permutation trinomials of the form x^rh(x ²^m−1 ) over the finite field F₂^2m using the permutation of the unit circle µ₂^m+1.

On Models of the Lie Algebra G_u,v and Euler Integral Transformation

Sarasvati Yadav — 2024-07-01

In this study, we framed two variable and three variable models of the irreducible representations of the Lie Algebra G_u,v. The two variable models are then transmuted in terms of difference-differential operators using the Euler integral transformation, whereas the three variable models are transmuted in terms of difference-differential operators using the two-fold Euler integral transformation. Then, various recurrence relations and generating functions are obtained using these models.

Generalized Absolute Convergence of Double Walsh-Fourier Series

K. N. Darji — 2024-07-01

In this paper, we obtain a sufficient condition for the generalized absolute convergence of the double Walsh-Fourier series of a function f of (ϕ, ψ)-(Λ¹ , Λ²)-bounded variation.

Ohno-Zagier Relation for Interpolated q-Multiple Zeta Values with Full Height

Nita Tamang — 2024-07-01

An algebraic approach has been employed to prove the Ohno-Zagier relation for interpolated q−multiple zeta values with full height.

On the Absolute Norlund Summability of Double Fourier Series

Prince Ashvinbhai Bhuva — 2024-07-01

In this paper, we give sufficient conditions for the absolute N¨orlund summability of double Fourier series. In particular, we get sufficient conditions for the absolute Ces`aro summability of double Fourier series. We also give sufficient conditions for regularity in the sense of Hardy of N¨orlund summability for a double sequence.

An Inverse and Derivative Free Regularized Iterative Scheme for Nonlinear ill-Posed Mootone Operators

D. Pradeep — 2024-07-01

In this paper, we consider an inverse and derivative-free regularized iterative scheme for solving nonlinear ill-posed problems involving monotone operators based on the contraction principle in the Hilbert space. We prove that the scheme converges to the Lavrentiev solution. The salient features of this scheme are: (i.) convergence analysis and desired convergence rate require only weaker assumptions compared to many assumptions used in the standard scheme in literature, (ii.) a parameter choice strategy that gives the same convergence rate as that of an priori method without using the source condition (iii.) computation of an optimal order regularization parameter O(δ^1/2) using the proposed parameter choice rule. Finally, we supply numerical examples to illustrate the proposed scheme. Further, we compare the numerical results of the proposed method with the standard method to demonstrate that our method achieves better computational output.

Effects of Human Population and Atmospheric Pollution on Rainfall: A Modeling Study

Gauri Agrawal — 2024-07-01

Rainfall is a well-known environmental process for the sustainability of water on the planet Earth, which maintains the hydrological cycle and fulfills the water demand for all living beings. In the last few decades, the impact of increasing human population and atmospheric pollutants on rainfall suppression has been observed. In the present work, we propose a mathematical model to assess the impact of human population and atmospheric pollution on rainfall. In the modeling process, it is assumed that the pollutants present in the atmosphere reduce the condensation and nucleation of cloud droplets to form raindrops, and formation rate of cloud droplets is a decreasing function of the human population. The model is analyzed using the stability theory of differential equations. Along with the analytical findings, we present the numerical simulation to validate the analytical findings of our proposed model system. The results obtained in this research uncover some key factors responsible for rainfall suppression.

Erratum and Addendum

Vivek Kumar Jain — 2024-07-01

Erratum and addendum to “On the Isomorphism Classes of Transversals III”, J. Indian Math. Soc., Vol. 82(3-4), (2015), 83-96.