scholarly journals Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
M. De la Sen
Keyword(s):  
Limit Cycles ◽  
Existence And Uniqueness ◽  
Contractive Condition ◽  
Uniformly Convex ◽  
Best Proximity Points ◽  
Uniformly Convex Banach Spaces ◽  
Pairwise Intersection ◽  
Finite Set ◽  
Uniqueness Of Limit Cycles ◽  
Number Of Iterations

This paper is devoted to investigating the limit properties of distances and the existence and uniqueness of fixed points, best proximity points and existence, and uniqueness of limit cycles, to which the iterated sequences converge, of single-valued, and so-called, contractive precyclic self-mappings which are proposed in this paper. Such self-mappings are defined on the union of a finite set of subsets of uniformly convex Banach spaces under generalized contractive conditions. Each point of a subset is mapped either in some point of the same subset or in a point of the adjacent subset. In the general case, the contractive condition of contractive precyclic self-mappings is admitted to be point dependent and it is only formulated on a complete disposal, rather than on each individual subset, while it involves a condition on the number of iterations allowed within each individual subset before switching to its adjacent one. It is also allowed that the distances in-between adjacent subsets can be mutually distinct including the case of potential pairwise intersection for only some of the pairs of adjacent subsets.

Best proximity points for p-cyclic summing iterated contractions

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3275-3287 ◽  
Author(s):  
Mihaela Petric ◽  
Boyan Zlatanov
Keyword(s):  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Uniformly Convex ◽  
Best Proximity Points ◽  
Uniformly Convex Banach Spaces ◽  
Cyclic Contractions ◽  
New Type

We generalize the p - summing contractions maps. We found sufficient conditions for these new type of maps, that ensure the existence and uniqueness of best proximity points in uniformly convex Banach spaces. We apply the result for Kannan and Chatterjea type cyclic contractions and we obtain sufficient conditions for these maps, that ensure the existence and uniqueness of best proximity points in uniformly convex Banach spaces.

scholarly journals Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
M. De la Sen ◽  
E. Karapinar
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Impulsive Differential Equations ◽  
The Self ◽  
Uniformly Convex ◽  
Convergence Properties ◽  
Best Proximity Points ◽  
Complete Metric Spaces ◽  
Uniformly Convex Banach Spaces

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

scholarly journals Some Results on Fixed and Best Proximity Points of Multivalued Cyclic Self-Mappings with a Partial Order

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Fixed Points ◽  
Partial Order ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Uniformly Convex ◽  
Best Proximity Points ◽  
Complete Metric Spaces ◽  
Uniformly Convex Banach Spaces ◽  
Nonempty Convex ◽  
Composite Self

This paper is devoted to investigate the fixed points and best proximity points of multivalued cyclic self-mappings on a set of subsets of complete metric spaces endowed with a partial order under a generalized contractive condition involving a Hausdorff distance. The existence and uniqueness of fixed points of both the cyclic self-mapping and its associate composite self-mappings on each of the subsets are investigated, if the subsets in the cyclic disposal are nonempty, bounded and of nonempty convex intersection. The obtained results are extended to the existence of unique best proximity points in uniformly convex Banach spaces.

scholarly journals Existence and Uniqueness of Limit Cycles in a Class of Planar Differential Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Khalil I. T. Al-Dosary
Keyword(s):  
Limit Cycles ◽  
Existence And Uniqueness ◽  
Differential Systems ◽  
Uniqueness Of Limit Cycles

This paper is an extension to the recent results presented by M. Sabatini about the existence and uniqueness of limit cycles of a certain class of planar differential systems in order to include other new classes. A concrete example exhibiting the applicability of the result is introduced.

scholarly journals On Best Proximity Results for a Generalized Modified Ishikawa’s Iterative Scheme Driven by Perturbed 2-Cyclic Like-Contractive Self-Maps in Uniformly Convex Banach Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
M. De la Sen ◽  
Mujahid Abbas
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Iterative Process ◽  
Iterative Scheme ◽  
Convex Banach Space ◽  
The Self ◽  
Uniformly Convex ◽  
Cyclic Structure ◽  
Best Proximity Points ◽  
Uniformly Convex Banach Spaces

This paper proposes a generalized modified iterative scheme where the composed self-mapping driving can have distinct step-dependent composition order in both the auxiliary iterative equation and the main one integrated in Ishikawa’s scheme. The self-mapping which drives the iterative scheme is a perturbed 2-cyclic one on the union of two sequences of nonempty closed subsets Ann=0∞ and Bnn=0∞ of a uniformly convex Banach space. As a consequence of the perturbation, such a driving self-mapping can lose its cyclic contractive nature along the transients of the iterative process. These sequences can be, in general, distinct of the initial subsets due to either computational or unmodeled perturbations associated with the self-mapping calculations through the iterative process. It is assumed that the set-theoretic limits below of the sequences of sets Ann=0∞ and Bnn=0∞ exist. The existence of fixed best proximity points in the set-theoretic limits of the sequences to which the iterated sequences converge is investigated in the case that the cyclic disposal exists under the asymptotic removal of the perturbations or under its convergence of the driving self-mapping to a limit contractive cyclic structure.

On the nonexistence, existence and uniqueness of limit cycles

Nonlinearity ◽  
1996 ◽  
Vol 9 (2) ◽  
pp. 501-516 ◽  
Author(s):  
H Giacomini ◽  
J Llibre ◽  
M Viano
Keyword(s):  
Limit Cycles ◽  
Existence And Uniqueness ◽  
Uniqueness Of Limit Cycles

scholarly journals The non-existence, existence and uniqueness of limit cycles for quadratic polynomial differential systems

2017 ◽  
Vol 149 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Jaume Llibre ◽  
Xiang Zhang
Keyword(s):  
Differential System ◽  
Limit Cycles ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Quadratic Polynomial ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Polynomial Differential System ◽  
Uniqueness Of Limit Cycles

AbstractWe provide sufficient conditions for the non-existence, existence and uniqueness of limit cycles surrounding a focus of a quadratic polynomial differential system in the plane.

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