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Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings : Applications to Impulsive Differential and Difference Equations
Joint Authors
Karapinar, Erdal
de La Sen, Manuel
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-10-29
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
de La Sen, Manuel& Karapinar, Erdal. 2013. Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings : Applications to Impulsive Differential and Difference Equations. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-16.
https://search.emarefa.net/detail/BIM-476974
Modern Language Association (MLA)
de La Sen, Manuel& Karapinar, Erdal. Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings : Applications to Impulsive Differential and Difference Equations. Abstract and Applied Analysis No. 2013 (2013), pp.1-16.
https://search.emarefa.net/detail/BIM-476974
American Medical Association (AMA)
de La Sen, Manuel& Karapinar, Erdal. Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings : Applications to Impulsive Differential and Difference Equations. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-16.
https://search.emarefa.net/detail/BIM-476974
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-476974