Dhage Iteration Method For Nonlinear First Order Measure integro-Differential Equations With Linear Perturbation

D. M. Suryawanshi; S.S. Bellale

doi:https://doi.org/10.14445/22315373/IJMTT-V64P518

International Journal of Mathematics Trends and Technology

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Volume 64 | Number 2 | Year 2018 | Article Id. IJMTT-V64P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V64P518

Dhage Iteration Method For Nonlinear First Order Measure integro-Differential Equations With Linear Perturbation

D. M. Suryawanshi , S.S. Bellale

Abstract

In this paper, the results of author proves the existence and uniqueness of solutions for the approximation of solutions to a nonlinear first order integro-differential equations using abstract measure theory. The approximation of the solutions are obtained under weaker mixed partial continuity and partial Lipschitz conditions. Our hypotheses and abstract results a real so solved by some numerical examples.

Keywords

Abstract measure differential equations, Dhage iteration methods, existence theorem, extremal solutions, approximation of solution, Abstract meseare integro differential equation. Hybrid fixed theorem.

References

[1] B.C. Dhage,Dhage iteration method for PBVPs of nonlinear first order hybrid integro-differential equations,Int.J.Nonlinearanal.Appli. 8 (2017) no.1, 95-112.
[2] B.C. Dhage, Quadratic perturbations of periodic boundary value problems of second order ordinary differentialequations, Differ. Equ. Appl. 2 (2010), 465-486.
[3] B.C. Dhage, and S.S. Bellale,Exitence theorem for perturbed Abstract measure differential equations. Non Linear Analysis 71 (2009) 319-328.
[4] B.C. Dhage, S.S. Bellale, Abstract measure integro differential equations. Global J. math Anal. 1(1-2) (2007) 91-108.
[5] B.C. Dhage, and S.S. Bellale,Exitence theorem for perturbed Abstract measure integro differential equations.Non Linear Theory; Methods and Applications (2008).11.057. The 15th International conference of International Academy of Physical Sciences Dec 9- 13,2012,Pathumthani, Thailand.
[6] D.M.Suryawanshi, S.S. Bellale, Iteration method for approximating solutions of perturbed abstract measure differential equations. Journal of Emerging Technologies and Innovative,746-752.
[7] S.S. Bellale, G.B. Dapke, Hybrid fixed point theorem for abstract measure Integro-differential equation, Intern. J. Math. Stat., 3 (1) (2018), 101-106.
[8] S.S. Bellale, S.B. Birajdar, On quadratic abstract measure integro differential equations, J.Comput. Modeling, 5 (3) (2015), 99-122.
[9] S.S. Bellale, S.B. Birajdar, D.S. Palimkar, Existence theorem for abstract measure delay integrodifferential equations, Appl. Comput. Math., 4(4) (2015), 225-231.
[10] B. C. Dhage, A new monotone iteration principle in the theory of nonlinear first order integro differential equations, Nonlinear Studies, 22(3)(2015), 397-417.
[11] B.C. Dhage, S.B. Dhage, J.R. Graef. Dhage iteration method for initial value problems for nonlinear first order hybrid integrodifferential equations, J. Fixed Point Theory Appl., 17(2016), 309-325.
[12] B.C.Dhage ,On abstract measure integro-differential equation , J Maths. Phys .Sci. 20 (1986) 367-380.
[13] S. Leela, stability of measure differential equation. Pacific J. Math 52 (2) (1974) 489-498.
[14] G.R.Shendge, S.R.Joshi, An abstract measure differential inequalities and applications, Acta Math. Hun 41(1983) 53-54
[15] D.Otrocol, I.A. Rus, Functional-differential equations with maxima of mixed type argument, Fixed Point Theory, 9(2008), no. 1, 207-220.
[16] B. C. Dhage, Hybrid fixed point theory in partially ordered normed linear spaces and applications to fractional integral equations, Differ. Equ Appl., 5(2013), 155-184.
[17] A. Granas, J. Dugundji, Fixed Point Theory, Springer Verlag, 2003.
[18] S. Heikkila, V. Lakshmikantham, Monotone Iterative Techniques for DiscontinuousNonlinear Differential Equations, Marcel Dekker inc., New York 1994.
[19] S.S. Bellale,Hybrid Fixed point theorem for abstract measure differential equation,WorldAcademy Of Science, Engineering and Technology,73 (2013) 782-785.

Citation :

D. M. Suryawanshi , S.S. Bellale, "Dhage Iteration Method For Nonlinear First Order Measure integro-Differential Equations With Linear Perturbation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 64, no. 2, pp. 115-129, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V64P518