arXiv subjects

Sumit Chandok

Publications and source records attributed to Sumit Chandok.

5 recordsLinked to original sources

arXiv2026

A modified double inertial subgradient extragradient algorithm for non-monotone variational inequality with applications

This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized half-space and a self-adaptive step-size rule which works without prior knowledge of the Lipschitz constant of the operator. We establish a weak convergence result for a variational inequality involving a non-monotone cost operator along with weak and strong convergence results for quasi-monotone and strongly pseudo-monotone operators, respectively. Under a simplified framework, linear convergence of the proposed method is also discussed. Additionally, we provide some numerical experiments to demonstrate the effectiveness of our iterative algorithm compared to previously established algorithms in solving real-world applications. Finally, we carry out a sensitivity analysis of our algorithm to demonstrate its effectiveness across various parameter settings.

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arXiv2025

Some inequalities related to Heinz mean constant with Birkhoff orthogonality

Motivated by the work of Baronti et al. [J. Math. Anal. Appl. 252(2000) 124-146], where they defined the supremum of an arithmetic mean of the side lengths of a triangle, summing antipodal points on the unit sphere, we introduce a new geometric constant for Banach spaces, utilizing the Heinz means that interpolate between the geometric and arithmetic means associated with Birkhoff orthogonality. We discuss the bounds in Banach spaces and find the values of constant in Hilbert spaces. We obtain the characterization of uniformly non-square spaces. We investigate the correlation between our notion of the Heinz mean constant and other well-known terms, viz., the modulus of convexity, modulus of smoothness, and rectangular constant. Furthermore, we also give a characterization of the Radon plane with an affine regular hexagonal unit sphere.

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arXiv2025

Convergence analysis for pseudo-monotone variational inequality problem involving projections onto a moving ball

This paper presents an iterative scheme that converges to the solution of a pseudo-monotone variational inequality problem in the setting of $\mathbb{R}^{n}$. Traditional methods often require projections onto the feasible set $\mathfrak{C}$ or onto a half-space containing $\mathfrak{C}$. However, computing projections onto a complicated feasible set can be difficult, and projections onto a half-space may fall outside $\mathfrak{C}$. Keeping this in mind, we aim to develop an iterative scheme that projects onto a ball that is contained in a feasible set and has an explicit expression. Our iterative scheme does not require prior knowledge of the Lipschitz constant of the cost operator. Finally, we provide some numerical experiments to show the effectiveness of our algorithm.

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arXiv2022

Geometric properties of a novel type of orthogonality via norm derivatives

In this article, we generalize the notion of orthogonality as a linear combination of norm derivatives in order to give a novel concept that we refer to as $\rho_{\alpha,\beta}$-orthogonality. Also, we discuss some of its geometric properties in a real normed linear space and present some sufficient criteria for the smoothness of a normed space by using $\rho_{\alpha,\beta}$-orthogonality. We provide a few examples to show that the $\rho_{\alpha,\beta}$- orthogonality cannot be compared to other well-known orthogonalities in any way. In addition to this, we offer a characterization of inner product spaces by making use of the functional notation $\rho_{\alpha,\beta}$. In addition, we show that any $\rho_{\alpha,\beta}$-orthogonality that preserves linear mapping between two normed linear spaces must necessarily be a scalar multiple of an isometry. Also, using the $\rho_{\alpha,\beta}$-functional, we define the idea of an angle between two vectors and talk about their characteristics in normed spaces.

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arXiv2017

Existence of fixed points for pairs of mappings and application to Urysohn integral equations

In this paper, we establish some common fixed point results for two pairs of weakly compatible mappings in the setting of $C$-complex valued metric space. Also, as application of the proved result, we obtain the existence and uniqueness of a common solution of the system of the Urysohn integral equations: \begin{eqnarray*} x(t)=\psi_i(t)+\int_{a}^{b}K_i(t,s,x(s))ds \end{eqnarray*} where $i=1, 2, 3, 4, a,b\in \mathbb{R}$ with $a\leq b, t\in [a,b], x, \psi_i\in C([a,b],\mathbb{R}^n)$ and $K_i:[a,b]\times [a,b]\times \mathbb{R}^n\rightarrow \mathbb{R}^n$ is a mapping for each $i=1, 2, 3, 4$.

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