# Articles

Some Modular Equations and Lambert Series for a Continued Fraction of Ramanujan -by Pramod Kumar Rawat

## Some Modular Equations and Lambert Series for a Continued Fraction of Ramanujan -by Pramod Kumar Rawat

Abstract: We give modular equations and Lambert Series for a continued fraction of Ramanujan. Keywords: Continued Fraction, Lambert Series, Modular Equation.   Download PDF               Download XML   How to cite this article: Pramod Kumar Rawat, Some Modular Equations and Lambert Series for a...

Sufficient condition of the Hopf bifurcation -by Amine Bernoussi

## Sufficient condition of the Hopf bifurcation -by Amine Bernoussi

Abstract: In this paper we propose a new sufficient condition for the Hopf bifurcation of equilibrium is derived for nonlinear autonomous differential equations with delay in three dimension, by analysis the characteristic equation. Keywords: Local stability and Bifurcation the Hopf.   Download PDF          ...

ON THE STABILITY OF HEPATITIS B VIRUS-HEPATITIS D VIRUS (HBV-HDV) CO-INFECTION WITH CONTROLS IN A DYNAMIC POPULATION -by Remigius Okeke Aja,Titus Ifeanyi Chinebu and Everestus Obinwanne Eze

## ON THE STABILITY OF HEPATITIS B VIRUS-HEPATITIS D VIRUS (HBV-HDV) CO-INFECTION WITH CONTROLS IN A DYNAMIC POPULATION -by Remigius Okeke Aja,Titus Ifeanyi Chinebu and Everestus Obinwanne Eze

Abstract: In this paper, the stability analysis of Hepatitis B virus - Hepatitis D virus (HBV-HDV) Co-infection with controls in a dynamic population was investigated using Jacobian method. The Jacobian matrix formed was evaluated numerically. The result showed that the equilibrium point of the solution is...

Approximate Solution of Cubic Nonlinear Stochastic Oscillators Under Parametric Excitations -by Osu, Bright. O, Eze, E. O and Ujumadu, R. N

## Approximate Solution of Cubic Nonlinear Stochastic Oscillators Under Parametric Excitations -by Osu, Bright. O, Eze, E. O and Ujumadu, R. N

Abstract: In this paper an approximate solution of cubic nonlinear stochastic oscillators under parametric excitations were investigated using Picard iterative procedure. The results presents the existence of the solution, and the solution. This improves and extends some results in literature. Keywords: Cubic non-linearity, Stochastic oscillators, Frequency of...

Qualitative Behavior of a Quadratic Second-Order Rational Difference Equation -by M. B. Almatrafi, E. M. Elsayed and Faris Alzahrani

## Qualitative Behavior of a Quadratic Second-Order Rational Difference Equation -by M. B. Almatrafi, E. M. Elsayed and Faris Alzahrani

Abstract: This article demonstrates the existence of boundedness, asymptotic behavior and the periodicity of the following quadratic second-order rational difference equation: \begin{equation*} x_{n+1}=ax_{n}+\dfrac{bx_{n}^{2}+cx_{n}x_{n-1}+dx_{n-1}^{2}}{\alpha x_{n}^{2}+\beta x_{n}x_{n-1}+\gamma x_{n-1}^{2}},\;\;\;n=0,1,..., \end{equation*} where the constants $a,\ b,\ c,\ d,\ \alpha ,\ \beta$ and $\gamma$ are positive real numbers and...

Method for solving Lane-Emden type differential equations by Coupling of wavelets and Laplace transform -by Jai Prakesh Jaiswal and Kailash Yadav

## Method for solving Lane-Emden type differential equations by Coupling of wavelets and Laplace transform -by Jai Prakesh Jaiswal and Kailash Yadav

Abstract: The objective of this paper is to obtain the numerical solution of Lane-Emden type equations by coupling method of Laplace transform and Chebyshev wavelets. By using the properties of Laplace transform and Chebyshev wavelets, an operational matrix is derived to convert the Lane-Emden equations into...

Some fixed point theorems on dislocated $b$-metric and dislocated quasi $b$-metric spaces -by P.G. Golhare and C. T. Aage

## Some fixed point theorems on dislocated $b$-metric and dislocated quasi $b$-metric spaces -by P.G. Golhare and C. T. Aage

Abstract: A. Branciari in his paper entitled(\cite{ref13}) \lq\lq A fixed point theorem for mappings satisfying a general contractive condition of integral type\rq\rq ~ has proved following theorem:  Let $(X,d)$ be a complete metric space, $c\in ]0,1[,$ and let $f:X\to X$ be a mapping such that for...

Further notions related to new operators and compactness via supra soft topological spaces -by M. E. El-Shafei, M. Abo-Elhamayel and T. M. Al-shami

## Further notions related to new operators and compactness via supra soft topological spaces -by M. E. El-Shafei, M. Abo-Elhamayel and T. M. Al-shami

Abstract: The first objective of this paper, is to study the properties of supra soft limit points with the help of a soft point notion and to introduce the notions of supra soft boundary and supra soft closure operators. With regard to these notions, we describe...

Dual Skew Semi-Heyting Almost Distributive Lattices -by Berhanu Assaye, Mihret Alamneh and Yeshiwas Mebrat

## Dual Skew Semi-Heyting Almost Distributive Lattices -by Berhanu Assaye, Mihret Alamneh and Yeshiwas Mebrat

Abstract: In this paper we introduce the concept of dual skew SHADLs and characterize it in terms of dual SHADL. We define an equivalence relation $\theta$ on a dual skew SHADL $L$ and prove that $\theta$ is a congruence relation on the equivalence class $[x]\theta$ so...

Some fixed point theorems in dislocated quasi $b$-metric spaces -by K P R Sastry and L Vijaya Kumar

## Some fixed point theorems in dislocated quasi $b$-metric spaces -by K P R Sastry and L Vijaya Kumar

Abstract: In this paper, we establish the common fixed point theorems in dislocated quasi $b$-metric spaces.Incidentally we obtain results of Aage and Golhare as corollaries. Keywords: Fixed point,dislocated metric,b-metric space,dislocated b-metric space,Banach Contraction, Kannan contraction.   DOWNLOAD PDF                 DOWNLOAD XML  ...

Decision Making with help of the Repeated Average Method of Fuzzy Soft Matrix -by M.K. Hasan, Md. Yasin Ali, AbedaSultana and N. K. Mitra

## Decision Making with help of the Repeated Average Method of Fuzzy Soft Matrix -by M.K. Hasan, Md. Yasin Ali, AbedaSultana and N. K. Mitra

Abstract: Most of our traditional tools for formal modeling, reasoning, and computing are crisp, deterministic, and precise in character. But many complicated problems in economics, engineering, environment, social science, medical science, etc., involve data which are not always all crisp. We cannot always use the classical...

Mazur ulam problems on 2- fuzzy 2- anti normed linear space -by Thangaraj Beaula and Beulah Mariya

## Mazur ulam problems on 2- fuzzy 2- anti normed linear space -by Thangaraj Beaula and Beulah Mariya

Abstract: In this paper , we introduce the concepts of 2-isometry, collinearity, Lipschitz mapping in 2-fuzzy 2-anti normed linear space and a theorem holds, when the 2-fuzzy 2-isometry which mapped to 2-fuzzy 2-anti normed linear space is affine. Keywords: 2-Strictly convex, 2-isometry, Lipschitz mapping, Area one preserving...

Fixed point results of integral type on complete $S_{b}$-metric space using $C$-class functions -by Langpoklakpam Premila Devi, Laishram Shambhu Singh

## Fixed point results of integral type on complete $S_{b}$-metric space using $C$-class functions -by Langpoklakpam Premila Devi, Laishram Shambhu Singh

Abstract: In this paper, we use $C$-class function to generalized the concept of a new contractive conditions of integral type on a complete $S_{b}$- metric space. Keywords: $S_{b}$-metric space, $C$-class functions and fixed point.   DOWNLOAD PDF               DOWNLOAD XML     How...

A study of generalized continuous functions -by Zeinab Bandpey and Bhamini M. P. Nayar

## A study of generalized continuous functions -by Zeinab Bandpey and Bhamini M. P. Nayar

Abstract: In the paper, Weak Continuity Forms, Graph Conditions and Applications, the concept of $u$-continuous functions are introduced and presented several applications of such functions. In the present study, by generalizing the concept of $u$-continuity using the notion of an $\alpha$-set, introduced by O. Njastad ,...

Coefficient bounds for a subclass of $m$ - fold symmetric bi-univalent functions with Chebyshev polynomial -by G.Thirupathi

## Coefficient bounds for a subclass of $m$ - fold symmetric bi-univalent functions with Chebyshev polynomial -by G.Thirupathi

Abstract: In this paper, we introduce two new subclasses of $\Sigma _{m}$ consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disk $\mathbb{U}$. Furthermore, we establish bounds for the coefficients for these subclasses. Keywords: Starlike and convex functions, Chebyshev polynomials, $m$-fold symmetric functions, coefficient...

One-Dimensional Solute Transport in a Heterogeneous Porous Media with Pulse Type Input Source -by R. R. Yadav and Joy Roy

## One-Dimensional Solute Transport in a Heterogeneous Porous Media with Pulse Type Input Source -by R. R. Yadav and Joy Roy

Abstract: An advection-dispersion equation subjected to temporally and spatially dependent groundwater velocity, dispersion coefficient along with a time dependent pulse type input of time varying nature is solved for one dimensional semi-infinite porous medium. Input concentration is any continuous smooth function of time acts up to...

Stability analysis of the transmission dynamics of hepatitis B Virus infection with controls in a population -by Remigius Okeke Aja and David Omale

## Stability analysis of the transmission dynamics of hepatitis B Virus infection with controls in a population -by Remigius Okeke Aja and David Omale

Abstract: In this paper, the stability in the occurrence of HB Virus in a population was considered. The equilibrium states were examined. The stability in the occurrence of the HB Virus was verified using the Jacobian method. It was shown that the disease occurrence is unstable...

Fixed point results of various cyclic contractions in metric spaces -by G V R Babu, K K M Sarma, V A Kumari and P Sudheer Kumar

## Fixed point results of various cyclic contractions in metric spaces -by G V R Babu, K K M Sarma, V A Kumari and P Sudheer Kumar

Abstract: In this paper, we introduce various cyclic contractions, namely $\varphi$-cyclic contractive mapping, almost Geraghty cyclic contraction mapping and almost $\psi$-cyclic contraction mapping. We prove the existence of fixed points of these maps in complete metric spaces. We draw some corollaries and provide examples in support...

A new computational method for smooth solution of first order nonlinear Cauchy problem -by A. Saravanan, N. Magesh and A. John Christopher

## A new computational method for smooth solution of first order nonlinear Cauchy problem -by A. Saravanan, N. Magesh and A. John Christopher

Abstract: A smooth solution of the first order nonlinear hyperbolic partial differential equation arising in transport phenomena is discussed. Although the method of characteristics is offered within the literature, it conjointly comes across some difficulties like it is valid only for first order hyperbolic partial differential...

Subadditive and completely monotonic properties of the tricomi confluent hypergeometric functions -by B. Ravi and A. Venkat Laxmi

## Subadditive and completely monotonic properties of the tricomi confluent hypergeometric functions -by B. Ravi and A. Venkat Laxmi

Abstract: In the paper, the authors establish some sub-additive and completely monotonic properties of the Tricomi confluent hypergeometric functions. As an application, authors derive some bounds for modified Bessel's function of the second kind. Keywords: Sub and Super-additive functions, Tricomi conuent hypergeometric function.   DOWNLOAD PDF    ...