Numerical Solution of a Quadratic Integral Equation through Classical Schauder Fixed Point Theorem
Numerical Solution of a Quadratic Integral Equation through Classical Schauder Fixed Point Theorem
In this paper, we investigate the existence of at least one solution on the closed interval for quadratic integral equations with non-linear modification of the argument in Hölder spaces using the technique in the classical Schauder fixed point theorem.
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- [1] M. Benchohra, M. A. Darwish, On unique Solvability of Quadratic Integral Equations with Linear Modification of the
Argument, Miskolc Math. Notes, 10 (2009), 3-10.
- [2] J. Banas, R. Nalepa, On the space of functions with growths tempered by a modulus of continuity and its applications, J.
Funct. Space Appl. (2013), 13 pages, doi:http://dx.doi.org/10.1155/2013/820437.
- [3] J. Caballero, M. Abdalla, K. Sadarangani, Solvability of a quadratic integral equation of fredholm type in H¨older spaces,
Electron. J. Differ. Eq., 31 (2014), 1-10.
- [4] J. Schauder, Der Fixpunktsatz in Funktionalriiumen, Studia Math., 2 (1930), 171-180.
- [5] J. Banas, A. Chlebowicz, On an elementrary inequality and its application in theory of integral equations, J. Math. Ineq.,
11 (2) (2017), 595-605.
- [6] J. Caballero, B. Lopez, K. Sadarangani, Existence of nondecreasing and continuous solutions of an integral equation with
linear modification of the argument, Acta Math. Sin. (Engl. Ser.), 23 (9) (2007), 1719-1728.
- [7] M. A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl., 311(1) (2005),112-119.
- [8] S. Hu, M. Khavanin, W. Zhuang, Integral equations arising in the kinetic theory of gases, Appl. Anal., 34 (1989),261-266.
- [9] C. A. Stuart, Existence theorems for a class of non-linear integral equations, Math. Z., 137 (1974) 49-66.
- [10] J. Banas, A. Chlebowicz, On existence of integrable solutions of a functional integral equation under Carath´eodory
conditions, Nonlinear Anal., 70 (2009), 3172-3179.
- [11] J. Bana´s, B. Rzepka, On local attractivity and asymptotic stability of solutions of a quadratic Volterra integral equation,
Appl. Math. Comput., 213 (2009), 102-111.
- [12] H. Deepmala, K. Pathak, A study on some problems on existence of solutions for nonlinear functional-integral equations,
Acta Math. Scientia, 33 (2013), 1305-1313.
- [13] H. Deepmala, K. Pathak, Study on existence of solutions for some nonlinear functional-integral equations with applications,
Math. Commun., 18 (2013), 97-107.
- [14] K. Maleknejad, K. Nouri, R. Mollapourasl, Existence of solutions for some nonlinear integral equations, Communications
in Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 2559-2564.
- [15] K. Maleknejad, K. Nouri, R. Mollapourasl, Investigation on the existence of solutions for some nonlinear functional-integral
equations, Nonlinear Anal., 71 (2009), 1575-1578.
- [16] L. N. Mishra, R. P. Agarwal, M. Sen, Solvability and asymptotic behavior for some nonlinear quadratic integral equation
involving Erd´elyi-Kober fractional integrals on the unbounded interval, Prog. Frac. Differ. Appli., 2 (3) (2016).
- [17] L. N. Mishra, M. Sen, On the concept of existence and local attractivity of solutions for some quadratic Volterra integral
equation of fractional order, Appl. Math. Comput., (2016), http://dx.doi.org/10.1016/j.amc.2016.03.002.
- [18] L. Liu, F. Guo, C. Wu, Y. Wu, Existence theorems of global solutions for nonlinear Volterra type integral equations in
Banach spaces, J. Math. Anal. Appl., 309 (2005), 638-649.
- [19] J. Mallet-Paret, R.D. Nussbam, Inequivalent measures of noncompactness and the radius of the essential spectrum, Proc.
Amer. Math. Soc., (2010), 917-930.
- [20] G. Micula, G. Fairweather, Direct numerical spline methods for first order Fredholm integro-differential equations, Rev.
Anal. Numer. Theory Approx., 22 (1) (1993), 59-66.
- [21] M. Mursaleen, S.A. Mohiuddine, Applications of noncompactness to the infinite system of differential equations in `p
spaces, Nonlinear Anal. Theory Methods Appl., 75 (4) (2012), 2111-2115.
- [22] L. Olszowy, Solvability of infinite systems of singular integral equations in Fr´echet space of continuous functions, Comp.
Math. Appl. 59 (2010), 2794-2801.
- [23] M. J. Caballero, R.Nalepa, K. Sadarangani, Solvability of a quadratic integral equation of Fredholm type with Supremum
in H¨older Spaces, J. Funct. Space Appl., (2014), 7 pages, doi:http://dx.doi.org/10.1155/2014/856183.