Existence and Uniqueness of Solution of Summation-Difference Equation of Finite Delay in Cone Metric Space

Authors

  • G. C. Done P. G. Department of Mathematics, N. E. S. Science College, Nanded
  • K. L. Bondar P. G. Department of Mathematics, Government Vidarbha Institute of Science and Humanities, Amaravati
  • P. U. Chopade Department of Mathematics, D. S. M.'s Arts, Commerce and Science College, Jintur

DOI:

https://doi.org/10.26713/cma.v11i3.1395

Keywords:

Difference equation, Summation equation, Existence of solution, Cone metric space, Banach contraction principle

Abstract

In this research article, we study the existence and uniqueness of solution of Summation-Difference equation of finite delay with nonlocal condition in cone metric space. The result is obtained by using the some extensions of Banach's contraction principle in complete cone metric space and also provide example to demonstrate of main result.

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References

M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, Journal of Mathematical Analysis and Applications 341(1) (2008), 416 – 420, DOI: 10.1016/j.jmaa.2007.09.070.

R. P. Agarwal, Difference Equations and Inequalities: Theory, Methods and Applications, Marcel-Dekker, New York (1991), URL https://doc.lagout.org/science/0_Computer%20Science/3_Theory/Mathematics/Difference%20Equations%20and%20Inequalities%20-%20Theory.pdf.

K. L. Bondar, Existence and uniqueness of results for first order difference equations, Journal of Modern Methods in Numerical Mathematical 2(1-2) (2011), 16 – 20, URL: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.682.2335&rep=rep1&type=pdf.

K. L. Bondar, On some summation-difference inequalities, International Journal of Mathematical Archive 2(9) (2011), 1608 – 1611, URL: http://ijma.info/index.php/ijma/article/viewFile/533/276.

K. L. Bondar, Uniqueness results for first order difference equations, International Journal of Pure and Applied Sciences and Technology 4(2) (2011), 57 – 62, URL: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.419.8444&rep=rep1&type=pdf.

K. L. Bondar and A. B. Jadhao, Local and global existence of solutions for summation equation, International Journal of Pure and Applied Sciences and Technology 13(1) (2012), 1 – 5, URL: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.419.9999&rep=rep1&type=pdf.

P. U. Chopade and K. L. Bondar, Existence of solutions to boundary value problem of functional difference equation, International Journal of Mathematica Analysis 5(13) (2011), 643 – 650, URL: http://www.m-hikari.com/ijma/ijma-2011/ijma-13-16-2011/chopadeIJMA13-16-2011.pdf.

S. G. Deo, V. Lakshmikantham and V. Raghavendra, Text Book of Ordinary Differential Equations, 2nd Edition, Tata McGraw-Hill Publishing Company Limited, New Delhi (2003).

G. C. Done, K. L. Bondar and P. U. Chopade, Existence and uniqueness of solution of first order nonlinear difference equation, Journal of Mathematical and Computational Science 10(5) (2020), 1375 – 1383, DOI: 10.28919/jmcs/4619.

G. C. Done, K. L. Bondar and P. U. Chopade, Existence and uniqueness results on mixed type summation-difference equations in cone metric space, Journal of Mathematical and Computational Science 10(4) (2020), 956 – 963, DOI: 10.28919/jmcs/4530.

L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, Journal of Mathematical Analysis and Applications 332(2) (2007), 1468 – 1476, DOI: 10.1016/j.jmaa.2005.03.087.

D. Ilic and V. Rakocevic, Common fixed points for maps on cone metric space, Journal of Mathematical Analysis and Applications 341(3) (2008), 876 – 882, DOI: 10.1016/j.jmaa.2007.10.065.

A. Karoui, On the existence of continuous solutions of nonlinear integral equations, Applied Mathematics Letters 18(3) (2005), 299 – 305, DOI: 10.1016/j.aml.2004.09.007.

W. G. Kelley and A. C. Peterson, Difference Equation, Academic Press (2001).

M. K. Kwong, On Krasnoselskii's cone fixed point theorems, Fixed Point Theory and Applications 2008 (2008), Article ID 164537, 18 pages, DOI: /10.1155/2008/164537.

P. Raja and S. M. Vaezpour, Some extensions of Banach's contraction principle in complete cone metric spaces, Fixed Point Theory and Applications 2008 (2008), Article ID 768294, 11 pages, DOI: 10.1155/2008/768294.

S. H. Vaezpour and R. Hamlbarani, Some notes on the paper Cone metric spaces and fixed point theorems of contractive mappings, Journal of Mathematical Analysis and Applications 345(2) (2008), 719 – 724, DOI: 10.1016/j.jmaa.2008.04.049.

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Published

30-09-2020
CITATION

How to Cite

Done, G. C., Bondar, K. L., & Chopade, P. U. (2020). Existence and Uniqueness of Solution of Summation-Difference Equation of Finite Delay in Cone Metric Space. Communications in Mathematics and Applications, 11(3), 325–334. https://doi.org/10.26713/cma.v11i3.1395

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Section

Research Article