Some Common Fixed Point Results in Cone Metric Spaces for Rational Contractions
Devnarayan Yadav,
Surendra Kumar Tiwari
Issue:
Volume 8, Issue 1, March 2022
Pages:
1-10
Received:
21 February 2022
Accepted:
15 March 2022
Published:
23 March 2022
Abstract: A very engrossing technique in theory of contractive mapping fixed point. A number of authors have defined contractive type mappings on a cone metric spaces X which are generalization of the well -known Banach contraction, and have the property that each of such mapping has a unique fixed point. The fixed point can always be found by using Picard Iteration, opening with initial choice x0∈X. In this manuscript, we generalize, extend and improve the result under the assumption of normality of cone for rational expression type contraction mapping in cone metric spaces. The present article is to provide a new alternative proof for two and three mapping and obtain the entity and exclusiveness of common fixed point. The concernment of the present paper to open a new direction of proof to be extended based on the methods of rational type contraction mapping in cone metric spaces of fixed-point theory. The assistance of this article is organized as follows. In section 2, preliminary notes. In this section we recall some standard notations and definitions which we needed. In section 3, the main results of the author are given. In this section we evidence of new results for two and three maps. In section 4, gives brief concluding note of the paper.
Abstract: A very engrossing technique in theory of contractive mapping fixed point. A number of authors have defined contractive type mappings on a cone metric spaces X which are generalization of the well -known Banach contraction, and have the property that each of such mapping has a unique fixed point. The fixed point can always be found by using Picard I...
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Continuous-Time Difference Equations and Distributed Chaos Modelling
Issue:
Volume 8, Issue 1, March 2022
Pages:
11-21
Received:
13 February 2022
Accepted:
29 March 2022
Published:
20 April 2022
Abstract: The article aims to attract the attention of researchers, experts and those interested in nonlinear dynamics and chaos theory to the not well known field of continuous-time difference equations, in the hopes of opening new doors into the study of chaotic system. Deterministic chaos and related notions are used in an increasing number of scientific works. There are a lot of problems associated with the mathematical aspects of the fine structure of chaos. Just as discrete-time difference equations have proven to be excellent models of temporal (discrete) chaos, so continuous-time difference equations provide new elegant mechanisms for onset and inside reconstructions of spatio-temporal (distributed) chaos. Distributed chaos is usually described by boundary value problems for partial differential equations. A number of these boundary value problems can be reduced to continuous-time difference equations, which enable one to build new chaos scenarios arising from the properties of the equations. Whereas the emergence of deterministic chaos is usually attributed to the complex structure of attractors, these new scenarios are based on a highly complex structure of spatially extended “points” of the attractor. Examples of reducible boundary value problems are set forth in the article, but the main focus is on a very elementary overview of the principal features of solutions of the simplest nonlinear continuous-time difference equations: loss of continuity, asymptotic periodicity, gradient catastrophe, fractal geometry, space-filling property, going beyond the horizon of predictability, self-stochasticity (deterministic solutions are asymptotically described by random processes), formation of hierarchical structures (down to arbitrarily small scales). Here we have a wonderful example of how very complex phenomena can be described with very simple equations. The use of continuous-time difference equations in the study of reducible and close-to-reducible boundary value problems migh help to advance in understanding possible mathematical mechanisms for distributed chaos.
Abstract: The article aims to attract the attention of researchers, experts and those interested in nonlinear dynamics and chaos theory to the not well known field of continuous-time difference equations, in the hopes of opening new doors into the study of chaotic system. Deterministic chaos and related notions are used in an increasing number of scientific ...
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