Existence of solutions of the dynamic cauchy problem in banach spaces

No Thumbnail Available

Date

2012

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Warsaw University

Research Projects

Organizational Units

Thumbnail Image
Organizational Unit
Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

Journal Issue

Abstract

In this paper we obtain the existence of solutions and Carathéodory type solutions of the dynamic Cauchy problem in Banach spaces for functions defined on time scales xδ(t) = f(t, x(t)), x(0) = x0, t 2 Ia, where f is continuous or f satisfies Carathéodory conditions and some conditions expressed in terms of measures of noncompactness. The Mönch fixed point theorem is used to prove the main result, which extends these obtained for real valued functions.

Description

Keywords

Banach space, Carathéodory solutions, Cauchy dynamic problem, Measure of noncompactness, Time scales

Turkish CoHE Thesis Center URL

Citation

8

WoS Q

Q1

Scopus Q

Source

Demonstratio Mathematica

Volume

45

Issue

3

Start Page

561

End Page

573

URI

https://doi.org/10.1515/dema-2013-0401
 https://hdl.handle.net/20.500.14411/3690

Collections

Scopus