scholarly journals Best Proximity Results with Applications to Nonlinear Dynamical Systems

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 900 ◽  
Author(s):  
Hamed H Al-Sulami ◽  
Nawab Hussain ◽  
Jamshaid Ahmad
Keyword(s):  
Approximate Solution ◽  
Global Minimum ◽  
Metric Spaces ◽  
Nonlinear Dynamical Systems ◽  
Best Proximity Point ◽  
Sufficient Conditions ◽  
Dynamical Programming ◽  
Ordered Metric Spaces ◽  
Nonlinear Dynamical ◽  
Multivalued Contraction

Best proximity point theorem furnishes sufficient conditions for the existence and computation of an approximate solution ω that is optimal in the sense that the error σ ( ω , J ω ) assumes the global minimum value σ ( θ , ϑ ) . The aim of this paper is to define the notion of Suzuki α - Θ -proximal multivalued contraction and prove the existence of best proximity points ω satisfying σ ( ω , J ω ) = σ ( θ , ϑ ) , where J is assumed to be continuous or the space M is regular. We derive some best proximity results on a metric space with graphs and ordered metric spaces as consequences. We also provide a non trivial example to support our main results. As applications of our main results, we discuss some variational inequality problems and dynamical programming problems.

scholarly journals Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Erdal Karapınar ◽  
V. Pragadeeswarar ◽  
M. Marudai
Keyword(s):  
Approximate Solution ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Optimal Approximate Solution ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
New Class

We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.

scholarly journals Best Proximity Point Results for Modified --Proximal Rational Contractions

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
N. Hussain ◽  
M. A. Kutbi ◽  
P. Salimi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Point Theory ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
New Concepts ◽  
Special Cases ◽  
Banach’S Contraction Principle

We first introduce certain new concepts of --proximal admissible and ---rational proximal contractions of the first and second kinds. Then we establish certain best proximity point theorems for such rational proximal contractions in metric spaces. As an application, we deduce best proximity and fixed point results in partially ordered metric spaces. The presented results generalize and improve various known results from best proximity point theory. Several interesting consequences of our obtained results are presented in the form of new fixed point theorems which contain famous Banach's contraction principle and some of its generalizations as special cases. Moreover, some examples are given to illustrate the usability of the obtained results.

scholarly journals The Existence of Cone Critical Point and Common Fixed Point with Applications

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Critical Point ◽  
Point Theorem ◽  
Metric Spaces ◽  
Nonlinear Dynamical Systems ◽  
Cone Metric Spaces ◽  
Nonlinear Dynamical ◽  
Cone Metric

We first establish some new critical point theorems for nonlinear dynamical systems in cone metric spaces or usual metric spaces, and then we present some applications to generalizations of Dancš-Hegedüs-Medvegyev's principle and the existence theorem related with Ekeland's variational principle, Caristi's common fixed point theorem for multivalued maps, Takahashi's nonconvex minimization theorem, and common fuzzy fixed point theorem. We also obtain some fixed point theorems for weakly contractive maps in the setting of cone metric spaces and focus our research on the equivalence between scalar versions and vectorial versions of some results of fixed point and others.

scholarly journals Some best proximity point results for multivalued mappings on partial metric spaces

2021 ◽  
Vol 25 (1) ◽  
pp. 99-111
Author(s):  
Mustafa Aslantas ◽  
Al-Zuhairi Abed
Keyword(s):  
Contraction Mapping ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Multivalued Mappings ◽  
Partial Metric ◽  
Multivalued Contraction ◽  
New Concepts ◽  
Partial Metric Spaces

In this paper, we introduce two new concepts of Feng-Liu type multivalued contraction mapping and cyclic Feng-Liu type multivalued contraction mapping. Then, we obtain some new best proximity point results for such mappings on partial metric spaces by considering Feng-Liu's technique. Finally, we provide examples to show the effectiveness of our results.

scholarly journals Lagrange and practical stability criteria for dynamical systems with nonlinear perturbations

2012 ◽  
Vol 22 (1) ◽  
pp. 43-58
Author(s):  
Assen Krumov
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Computer Control ◽  
Nonlinear Dynamical System ◽  
Sufficient Conditions ◽  
Practical Stability ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Nonlinear Operators ◽  
Nonlinear Dynamical

Lagrange and practical stability criteria for dynamical systems with nonlinear perturbationsIn the paper two classes of nonlinear dynamical system with perturbations are considered. The sufficient conditions for robust Lagrange and practical stability are proven with theorems, applying the theory of nonlinear operators of the functional analysis. The presented criteria give also the bounds of the analyzed dynamical processes. Three examples comparing the numerical computer solutions and the analytical investigation of the stability of the systems are given. The method can be applied to analytical and computer modeling of nonlinear dynamical systems, synthesis of computer control and optimization.

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