Prashant Patel
@vidwan.inflibnet.ac.in
Assistant Professor
VIT-AP University
RESEARCH, TEACHING, or OTHER INTERESTS
Mathematics, Analysis, Control and Optimization
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
Prashant Patel and Rahul Shukla
Springer Science and Business Media LLC
AbstractThe aim of this paper to present some weak and strong convergence results for countable family of non-self mappings. More precisely, we employ the Mann–Dotson’s algorithm to approximate common fixed points of a countable family of non-self k-strict Pseudocontractive mappings in q-uniformly smooth Banach spaces.
Prashant Patel and Rahul Shukla
Walter de Gruyter GmbH
Abstract The aim of this article is to present some Δ \\Delta -convergence and strong convergence results for a countable family of non-self mappings. More precisely, we employ Mann-Dotson’s algorithm to approximate, common fixed points of a countable family of non-self L n {L}_{n} -Lipschitz mappings in hyperbolic metric spaces.
Rajendra Pant, Prashant Patel, Rahul Shukla, and Manuel De la Sen
MDPI AG
In this paper, we present some fixed point results for a class of nonexpansive type and α-Krasnosel’skiĭ mappings. Moreover, we present some convergence results for one parameter nonexpansive type semigroups. Some non-trivial examples have been presented to illustrate facts.
Prashant Patel and Rajendra Pant
National Library of Serbia
In this article, we present viscosity approximation methods for finding a common point of the set of solutions of a variational inequality problem and the set of fixed points of a multi-valued quasinonexpansive mapping in a Banach space. We also discuss some examples to illustrate facts and study the convergence behaviour of the iterative schemes presented herein, numerically.
Rajendra Pant, Rahul Shukla, and Prashant Patel
Springer Nature Singapore
Rajendra PANT, Prashant PATEL, and Rahul SHUKLA
Erdal Karapinar
Abstract. In this paper, we present some new fixed point results for a well-known class of generalized nonexpansive type mappings and associated Krasnosel'ski type mappings in Banach spaces. Further, we consider Mann type iteration for finding a common fixed point of a nonexpansive type semigroup. We also present a couple of nontrivial examples to illustrate facts and show numerical convergence.
Prashant Patel, Prashant Kumar, and Rajni
AIP Publishing
In the last many years for coastal regions the prediction of waves is still a big challenge for scientists. Many times, wave transformation harms the property and humans near coastal regions. To produce the exact numerical simulation of wave disturbances within bathymetry requires consideration of both dispersive and nonlinear waves in order to get physical effects. The current numerical model contains all these effects with variable bathymetry with Bossiness equation. Bossiness equation is used to determine the non-linear transformation of water surface waves in coastal region with the effects of shoaling, diffraction, reflection and refraction. Linear dispersion relations are determined in different form of the velocity variables. It improves the dispersion properties of the linear Boussinesq equations significantly, allowing them applicable to a larger water depth ranges. Nonlinear Boussinesq equations are used for describing the shallow water waves in intermediate water depth and dissemination of strong linear waves in surfing areas where breaking of the wave dominates. The Adams-Bashfourth (AB) predictor-corrector method is utilized to solve the non-linear Boussinesq equation. The validation of the numerical solution is compared with previous studies and experimental data. Further, the current numerical approach can be utilized for practical application in realistic situations.
Gulshan, Prashant Kumar, Prashant Patel, Rupali, and Sukhwinder Kaur
Author(s)
The mathematical model is presented to analyze the wave spectrum inside Paradip port under the resonance conditions with partial reflection, diffraction and refraction. During the extreme weather conditions, Paradip port have experienced the extreme ocean wave 3∼5 m in surface height. In irregular domain, the solution of Laplace equation along with partial refection condition on quays and breakwaters is obtained by using 3-D Boundary Element Method (3-D BEM). To validation, the present numerical scheme result is compared with the experimental data of Ippen & Goda (1963) and Lee (1971). Six record stations are located inside the port based on moored ship terminals. At these locations, the wave spectrum is computed by utilizing the Fast Fourier Transform (FFT) for the surface waves obtained in Paradip port.