Showing papers by "Vivek Kumar published in 2016"
TL;DR: In this paper, the convergence, stability, and data dependence of the Jungck-Khan iterative scheme for a pair of non-self operators are established for the special case Jungck Ishikawa and Jungck Mann iterative schemes.
Abstract: The Jungck–Khan iterative scheme for a pair of nonself operators contains as a special case Jungck–Ishikawa and Jungck–Mann iterative schemes. In this paper, we establish improved results about convergence, stability, and data dependence for the Jungck–Khan iterative scheme.
15 citations
TL;DR: In this article, a new stage structured prey-predator model with linear functional response is proposed and studied, which consists of three nonlinear ordinary differential equations to describe the interaction among juvenile prey, adult prey and predator populations.
Abstract: In this paper, a new stage structured prey-predator model with linear functional response is proposed and studied. The stages for prey have been considered. The proposed mathematical model consists of three nonlinear ordinary differential equations to describe the interaction among juvenile prey, adult prey and predator populations. The model is analyzed by using linear stability analysis to obtain the conditions for which our model exhibits stability around the possible equilibrium points. Besides this a rigorous global stability analysis has been performed for our proposed model by using Li and Muldowney approach (geometric approach). Global stability conditions for the proposed model are described in the form of theorem. This is not a case study, hence the real parameters are not available for this model. However, model may be simulated by using hypothetical set of parameters. Investigation of real parameters for the proposed model is an open problem.
14 citations
TL;DR: In this paper, strong convergence and stability results of a three-step random iterative scheme with errors for strongly pseudo-contractive Lipschitzian maps are established in real Banach spaces.
Abstract: In this work, strong convergence and stability results of a three step random iterative scheme with errors for strongly pseudo-contractive Lipschitzian maps are established in real Banach spaces. Analytic proofs are supported by providing numerical examples. Applications of random iterative schemes with errors to find solution of nonlinear random equation are also given. Our results improve and establish random generalization of results obtained by Xu and Xie [Y. Xu, F. Xie, Rostock. Math. Kolloq., 58 (2004), 93–100], Gu and Lu [F. Gu, J. Lu, Math. Commun., 9 (2004), 149–159], Liu et al. [Z. Liu, L. Zhang, S. M. Kang, Int. J. Math. Math. Sci., 31 (2002), 611–617] and many others. c ©2016 All rights reserved.
8 citations
TL;DR: In this article, the authors studied the convergence and stability of a new two-step random iterative scheme with errors for accretive Lipschitzian mapping in real Banach spaces.
Abstract: In this paper, we study the strong convergence and stability of a new two step random iterative scheme with errors for accretive Lipschitzian mapping in real Banach spaces. The new iterative scheme is more acceptable because of much better convergence rate and less restrictions on parameters as compared to random Ishikawa iterative scheme with errors. We support our analytic proofs by providing numerical examples. Applications of random iterative schemes with errors to variational inequality are also given. Our results improve and establish random generalization of results obtained by Chang [4], Zhang [31] and many others.
7 citations