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Ravi P. Agarwal

Publications and source records attributed to Ravi P. Agarwal.

At least 19 recordsLinked to original sources
arXiv2023

Existence and multiplicity for fractional Dirichlet problem with $γ(ξ)$-Laplacian equation and Nehari manifold

This paper is divided in two parts. In the first part, we prove coercivity results and minimization of the Euler energy functional. In the second part, we focus on the existence and multiplicity of a positive solution of fractional Dirichlet problem involving the $γ(ξ)$-Laplacian equation with non-negative weight functions in $\mathcal{H}^{α,β;χ}_{γ(ξ)}(Λ,\mathbb{R})$ using some variational techniques and Nehari manifold.

math.GM↗
arXiv2023

Hankel determinant for a general subclass of m-fold symmetric bi-univalent functions defined by Ruscheweyh operator

Making use of the Hankel determinant and the Ruscheweyh derivative, in this work, we consider a general subclass of m-fold symmetric normalized bi-univalent functions defined in the open unit disk. Moreover, we investigate the bounds for the second Hankel determinant of this class and some consequences of the results are presented. In addition, to demonstrate the accuracy on some functions and conditions, most general programs are written in Python V.3.8.8 (2021).

math.CV↗
arXiv2023

Uncertainty principles associated with the short time quaternion coupled fractional Fourier transform

In this paper, we extend the coupled fractional Fourier transform of a complex valued functions to that of the quaternion valued functions on $\mathbb{R}^4$ and call it the quaternion coupled fractional Fourier transform (QCFrFT). We obtain the sharp Hausdorff-Young inequality for QCFrFT and obtain the associated Rènyi uncertainty principle. We also define the short time quaternion coupled fractional Fourier transform (STQCFrFT) and explore its important properties followed by the Lieb's and entropy uncertainty principles.

math.GM↗
arXiv2023

A New Shrinking projection Algorithm for an infinite family of Bregman weak relatively nonexpansive mappings in a Banach Space

In this paper, using a new shrinking projection method and generalized resolvents of maximal monotone operators and generalized projections, we consider the strong convergence for finding a common point of the fixed points of a Bregman quasi-nonexpansive mapping, and common fixed points of a infinite family of Bregman weak relatively nonexpansive mappings, and common zero points of a finite family of maximal monotone mappings, and common solutions of an equilibrium problem in a reflexive Banach space.

math.FA↗
arXiv2022

A Simple proof for Imnang's algorithms

In this paper, a simple proof of the convergence of the recent iterative algorithm by relaxed $(u, v)$-cocoercive mappings due to S. Imnang [S. Imnang, Viscosity iterative method for a new general system of variational inequalities in Banach spaces. J. Inequal. Appl., 249:18 pp., 2013.] is presented.

math.FA↗
arXiv2021

A strong convergence theorem for solving an equilibrium problem and a fixed point problem using the Bregman distance

In this paper, using the Bregman distance, we introduce a new projection-type algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points. Then the strong convergence of the sequence generated by the algorithm will be established under suitable conditions. Finally, using MATLAB software, we present a numerical example to illustrate the convergence performance of our algorithm.

math.OC↗
arXiv2021

A simple proof for Kazmi et al.'s iterative scheme

In this paper, a simple proof for the existence iterative scheme by using two Hilbert spaces due to Kazmi et al. [K. R. Kazmi, R. Ali, M. Furkan, Hybrid iterative method for split monotone \ldots, Numer Algor, 2017] is provided.

math.FA↗
arXiv2021

Existence of group nonexpansive retractions and ergodic theorems in topological groups

Suppose that $G$ is a topological group and $ C $ a compact subset of $G$. In this paper we define group nonexpansive mappings and then we consider $\sc = \{T_{i} : i \in I \}$ as a family of the group nonexpansive mappings on $C$. Also we study the existence of group nonexpansive retractions $P_{i}$ from $C$ onto $\text{Fix}(\sc)$ such that $P_{i}T_{i} = T_{i}P_{i} = P_{i}$.

math.FA↗
arXiv2021

A Simple proof for the algorithms of relaxed $(u, v)$-cocoercive mappings and $α$-inverse strongly monotone mappings

In this paper, a simple proof is presented for the convergence of the algorithms for the class of relaxed $(u, v)$-cocoercive mappings and $α$-inverse strongly monotone mappings. Based on $α$-expansive maps, for example, a simple proof of the convergence of the recent iterative algorithms by relaxed $(u, v)$-cocoercive mappings due to Kumam-Jaiboon is provided. Also a simple proof for the convergence of the iterative algorithms by inverse-strongly monotone mappings due to Iiduka-Takahashi in a special case is provided. These results are an improvement as well as a refinement of previously known results.

math.FA↗
arXiv2021

Bicomplex Mittag-Leffler Function and Properties

With the increasing importance of the Mittag-Leffler function in the physical applications, these days many researchers are studying various generalizations and extensions of the Mittag-Leffler function. In this paper efforts are made to define bicomplex extension of the Mittag-Leffler function and also its analyticity and region of convergence are discussed. Various properties of the bicomplex Mittag-Leffler function including integral representation, recurrence relations, duplication formula and differential relations are established.

math.CV↗
arXiv2021

Pattern Formation Study of an Eco-epidemiological Model with Cannibalism and Disease in Predator Population

Pattern formation analysis of eco-epidemiological models with cannibalism and disease has been less explored in the literature. Therefore, motivated by this, we have proposed a diffusive eco-epidemiological model and performed pattern formation analysis in the model system. Sufficient conditions for local asymptotic stability and global asymptotic stability for the constant positive steady state are obtained by linearization and Lyapunov function technique. A priori estimate for the positive steady state is obtained for the nonexistence of the nonconstant positive solution using Cauchy and Poincaré inequality. The existence of the nonconstant positive steady states is studied using Leray-Schauder degree theory. The importance of the diffusive coefficients which are responsible for the appearance of stationary patterns is observed. Pattern formation is done using numerical simulation. Further, the effect of the cannibalism and disease are observed on the dynamics of the proposed model system. The movements of prey and susceptible predator plays a significant role in pattern formation. These movements cause stationary and non-stationary patterns. It is observed that an increment in the movement of the susceptible predator as well as cannibalistic attack rate converts non-Turing patterns to Turing patterns. Lyapunov spectrum is calculated for quantification of stable and unstable dynamics. Non-Turing patterns obtained with parameter set having unstable limit cycle are more interesting and realistic than stationary patterns. Stationary and non-stationary non-Turing patterns are obtained.

math.AP↗
arXiv2020

A regularity criterion in weak spaces to Boussinesq equations

In this paper, we study regularity of weak solutions to the incompressible Boussinesq equations in $\mathbb{R}^{3}\times (0,T)$. The main goal is to establish the regularity criterion in terms of one velocity component and the gradient of temperature in Lorentz spaces.

math.AP↗
arXiv2019

Regions of existence for a class of nonlinear diffusion type problems

The regions of existence are established for a class of two point nonlinear diffusion type boundary value problems (NDBVP) \begin{eqnarray*} &&\label{abst-intr-1} -s''(x)-ns'(x)-\frac{m}{x}s'(x)=f(x,s), \qquad m>0,~n\in \mathbb{R},\qquad x\in(0,1),\\ &&\label{abst-intr-2} s'(0)=0, \qquad a_{1}s(1)+a_{2}s'(1)=C, \end{eqnarray*} where $a_{1}>0,$ $a_{2}\geq0,~ C\in\mathbb{R}$. These problems arise very frequently in many branches of engineering, applied mathematics, astronomy, biological system and modern science (see \cite{Gatica1989, GRAY1980, Baxley1991, Chandershekhar1939, Duggan1986, Chambre1952}). By using the concept of upper and lower solutions with monotone constructive technique, we derive some sufficient conditions for existence in the regions where $\frac{\partial f}{\partial s}\geq0$ and $\frac{\partial f}{\partial s}\leq0$. Theoretical methods are applied for a set of problems which arise in real life.

math.CA↗
arXiv2019

On a seventh order convergent weakly $L$-stable Newton Cotes formula with application on Burger's equation

In this paper we derive $7^{th}$ order convergent integration formula in time which is weakly $L$-stable. To derive the method we use, Newton Cotes formula, fifth-order Hermite interpolation polynomial approximation (osculatory interpolation) and sixth-order explicit backward Taylor's polynomial approximation. The vector form of this formula is used to solve Burger's equation which is one dimensional form of Navier-Stokes equation. We observe that the method gives high accuracy results in the case of inconsistencies as well as for small values of viscosity, e.g., $10^{-3}$. Computations are performed by using Mathematica 11.3. Stability and convergence of the schemes are also proved. To check the efficiency of the method we considered 6 test examples and several tables and figures are generated which verify all results of the paper.

math.NA↗
arXiv2018

Geodesic Sandwich Theorem with an Application

The main goal of the paper is to prove the sandwich theorem for geodesic convex functions in a complete Riemannian manifold. Then by using this theorem we have proved an inequality in a manifold with bounded sectional curvature. Finally, we have shown that the gradient of a convex function is orthogonal to the tangent vector at some point of any geodesic.

math.DG↗
arXiv2017

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered.

math.OC↗
arXiv2017

Existence and concentration of positive ground state solutions for nonlinear fractional Schrödinger-Poisson system with critical growth

In this paper, we study the following fractional Schrödinger-Poisson system involving competing potential functions \begin{equation*} \left\{ \begin{array}{ll} \varepsilon^{2s}(-Δ)^su+V(x)u+ϕu=K(x)f(u)+Q(x)|u|^{2_s^{\ast}-2}u, & \hbox{in $\mathbb{R}^3$,} \varepsilon^{2t}(-Δ)^tϕ=u^2,& \hbox{in $\mathbb{R}^3$,} \end{array} \right. \end{equation*} where $\varepsilon>0$ is a small parameter, $f$ is a function of $C^1$ class, superlinear and subcritical nonlinearity, $2_s^{\ast}=\frac{6}{3-2s}$, $s>\frac{3}{4}$, $t\in(0,1)$, $V(x)$ $K(x)$ and $Q(x)$ are positive continuous function. Under some suitable assumptions on $V$, $K$ and $Q$, we prove that there is a family of positive ground state solutions with polynomial growth for sufficiently small $\varepsilon>0$, of which it is concentrating on the set of minimal points of $V(x)$ and the sets of maximal points of $K(x)$ and $Q(x)$. The methods are based on the Nehari manifold, arguments of Brezis-Nirenberg and concentration compactness of P. L. Lions.

math.AP↗