Existence Theorem for Abstract Measure Delay Integro-Differential Equations

S. S. Bellale; S. B. Birajdar; D. S. Palimkar

doi:doi:10.11648/j.acm.20150404.11

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Existence Theorem for Abstract Measure Delay Integro-Differential Equations

S. S. Bellale, S. B. Birajdar, D. S. Palimkar

Published in Applied and Computational Mathematics (Volume 4, Issue 4)

Received: 17 May 2015 Accepted: 1 June 2015 Published: 25 June 2015

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Abstract

In this paper, we have proved the existence and uniqueness results for an abstract measure delay integro-differential equation by using Leray-Schauder nonlinear alternative under certain Caratheodory conditions. The various aspects of the solutions of the abstract measure integro-differential equations have been studied in the literature using the various fixed point techniques such as Schauder,s fixed point principle and Banach contraction mapping principal etc. In this paper we have proved existence and uniqueness condition for Abstract Measure delay integro-differential equations.

Published in	Applied and Computational Mathematics (Volume 4, Issue 4)
DOI	10.11648/j.acm.20150404.11
Page(s)	225-231
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Time Scale, Abstract Measure Integro-Differential Equation, Abstract Measure Delay Integro-Differential Equation, Existence Theorem and Extermal Solutions

References

[1]	B. C. Dhage “On abstract measure integro-differential equations”, J. Math. Phy. Sci.20 (1986), 367 – 380
[2]	B. C. Dhage “On system of abstract measure integro – differential inequations and applications”, Bull. Inst. Math. Acad. Sinica18 (1989), 65 – 75
[3]	B. C. Dhage “Mixed monotonicity theorems for a system of abstract of measure delay integro – differential equations”, An. Stint. Univ. “Al. I. Cuza” IasiXLII (1996) 355 – 366
[4]	B. C. Dhage and S. S. Bellale, “Abstract measure integro – differential equations”, Global Jour Math. Anal.1 (2007), 91 – 108.
[5]	B. C. Dhage and S. S. Bellale, “Existence theorem for per- turbd abstract measure differential equations”, Nonlinear Analysis, 71(2009),e319-e328
[6]	S. S. Bellale, “Hybrid Fixed Point Theorem For Abstract Measure Differential Equation”, World Academy Of Science, Engineering and Technology, 73(2013) 782-785 ISSN- e2010-3778
[7]	B. C. Dhage, D. N. Chate and S. K. Ntouyas, “Abstract measure differential equations”, Dynamic Systems & Appl. 13 (2004) 105 – 108.
[8]	J. Dagudji and A. Granas, “Fixed point Theory”, Monograhie Math. PNW. Warsaw 1982.
[9]	S. R. Joshi, “A system of abstract measure delay differential equations”, J. Math. Phy. Sci. 13 (1979), 496 – 506.
[10]	S. R. Joshi and S. G. Deo, “On abstract measure delay differential equations”, An. Stint. Univ. Al I. CuzaIassiXXVI (1980), 327 – 335.
[11]	W. Rudin, “Real and Complex, Analysis, McGraw”, – Hill Inc.New York, 1966.
[12]	R. R. Sharma, “An abstract measure differential equation”, Proc, Amer, Math. Soc. 32 (1972) 503 – 510.
[13]	R. R. Sharma, “A measure differential inequality with applications”, Proc. Amer. Math. Soc. 48 (1975) 87 – 97.
[14]	G. R. Shendge and S. R. Joshi, “Abstract measure differential inequalities and applications”, Acta Math Hung. 41 (1983), 53 – 54.
[15]	D. R. Smart, “Fixed point Theorems”, Cambridge Unive. Press, Cambridge 1974.

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APA Style

S. S. Bellale, S. B. Birajdar, D. S. Palimkar. (2015). Existence Theorem for Abstract Measure Delay Integro-Differential Equations. Applied and Computational Mathematics, 4(4), 225-231. https://doi.org/10.11648/j.acm.20150404.11

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ACS Style

S. S. Bellale; S. B. Birajdar; D. S. Palimkar. Existence Theorem for Abstract Measure Delay Integro-Differential Equations. Appl. Comput. Math. 2015, 4(4), 225-231. doi: 10.11648/j.acm.20150404.11

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AMA Style

S. S. Bellale, S. B. Birajdar, D. S. Palimkar. Existence Theorem for Abstract Measure Delay Integro-Differential Equations. Appl Comput Math. 2015;4(4):225-231. doi: 10.11648/j.acm.20150404.11

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@article{10.11648/j.acm.20150404.11,
  author = {S. S. Bellale and S. B. Birajdar and D. S. Palimkar},
  title = {Existence Theorem for Abstract Measure Delay Integro-Differential Equations},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {4},
  pages = {225-231},
  doi = {10.11648/j.acm.20150404.11},
  url = {https://doi.org/10.11648/j.acm.20150404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150404.11},
  abstract = {In this paper, we have proved the existence and uniqueness results for an abstract measure delay integro-differential equation by using Leray-Schauder nonlinear alternative under certain Caratheodory conditions. The various aspects of the solutions of the abstract measure integro-differential equations have been studied in the literature using the various fixed point techniques such as Schauder,s fixed point principle and Banach contraction mapping principal etc. In this paper we have proved existence and uniqueness condition for Abstract Measure delay integro-differential equations.},
 year = {2015}
}

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TY  - JOUR
T1  - Existence Theorem for Abstract Measure Delay Integro-Differential Equations
AU  - S. S. Bellale
AU  - S. B. Birajdar
AU  - D. S. Palimkar
Y1  - 2015/06/25
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150404.11
DO  - 10.11648/j.acm.20150404.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
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EP  - 231
PB  - Science Publishing Group
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AB  - In this paper, we have proved the existence and uniqueness results for an abstract measure delay integro-differential equation by using Leray-Schauder nonlinear alternative under certain Caratheodory conditions. The various aspects of the solutions of the abstract measure integro-differential equations have been studied in the literature using the various fixed point techniques such as Schauder,s fixed point principle and Banach contraction mapping principal etc. In this paper we have proved existence and uniqueness condition for Abstract Measure delay integro-differential equations.
VL  - 4
IS  - 4
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Author Information

S. S. Bellale

Mathematics Research Centre, Dayanand Science College, Maharashtra, India
S. B. Birajdar

Department of Mathematics, Bidve Engineering College, Latur, Maharashtra, India
D. S. Palimkar

Department of Mathematics, Vasantrao Naik College, Nanded, Maharashtra, India

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APA Style

S. S. Bellale, S. B. Birajdar, D. S. Palimkar. (2015). Existence Theorem for Abstract Measure Delay Integro-Differential Equations. Applied and Computational Mathematics, 4(4), 225-231. https://doi.org/10.11648/j.acm.20150404.11

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ACS Style

S. S. Bellale; S. B. Birajdar; D. S. Palimkar. Existence Theorem for Abstract Measure Delay Integro-Differential Equations. Appl. Comput. Math. 2015, 4(4), 225-231. doi: 10.11648/j.acm.20150404.11

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AMA Style

S. S. Bellale, S. B. Birajdar, D. S. Palimkar. Existence Theorem for Abstract Measure Delay Integro-Differential Equations. Appl Comput Math. 2015;4(4):225-231. doi: 10.11648/j.acm.20150404.11

Copy | Download

@article{10.11648/j.acm.20150404.11,
  author = {S. S. Bellale and S. B. Birajdar and D. S. Palimkar},
  title = {Existence Theorem for Abstract Measure Delay Integro-Differential Equations},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {4},
  pages = {225-231},
  doi = {10.11648/j.acm.20150404.11},
  url = {https://doi.org/10.11648/j.acm.20150404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150404.11},
  abstract = {In this paper, we have proved the existence and uniqueness results for an abstract measure delay integro-differential equation by using Leray-Schauder nonlinear alternative under certain Caratheodory conditions. The various aspects of the solutions of the abstract measure integro-differential equations have been studied in the literature using the various fixed point techniques such as Schauder,s fixed point principle and Banach contraction mapping principal etc. In this paper we have proved existence and uniqueness condition for Abstract Measure delay integro-differential equations.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Existence Theorem for Abstract Measure Delay Integro-Differential Equations
AU  - S. S. Bellale
AU  - S. B. Birajdar
AU  - D. S. Palimkar
Y1  - 2015/06/25
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150404.11
DO  - 10.11648/j.acm.20150404.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 225
EP  - 231
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150404.11
AB  - In this paper, we have proved the existence and uniqueness results for an abstract measure delay integro-differential equation by using Leray-Schauder nonlinear alternative under certain Caratheodory conditions. The various aspects of the solutions of the abstract measure integro-differential equations have been studied in the literature using the various fixed point techniques such as Schauder,s fixed point principle and Banach contraction mapping principal etc. In this paper we have proved existence and uniqueness condition for Abstract Measure delay integro-differential equations.
VL  - 4
IS  - 4
ER  -

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