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Numerical Solution of a Quadratic Integral Equation through Classical Schauder Fixed Point Theorem

Yıl 2021, , 39 - 45, 29.03.2021

Merve Temizer Ersoy

https://doi.org/10.33434/cams.860254
Cited By: 1

Öz

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.

Anahtar Kelimeler

Hölder condition integral equation schauder fixed point theorem

Kaynakça

  • [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.

Yıl 2021, , 39 - 45, 29.03.2021

Merve Temizer Ersoy

https://doi.org/10.33434/cams.860254
Cited By: 1

Öz

Kaynakça

  • [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.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Merve Temizer Ersoy 0000-0003-4364-9144

Yayımlanma Tarihi 29 Mart 2021
Gönderilme Tarihi 13 Ocak 2021
Kabul Tarihi 10 Mart 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Temizer Ersoy, M. (2021). Numerical Solution of a Quadratic Integral Equation through Classical Schauder Fixed Point Theorem. Communications in Advanced Mathematical Sciences, 4(1), 39-45. https://doi.org/10.33434/cams.860254
AMA Temizer Ersoy M. Numerical Solution of a Quadratic Integral Equation through Classical Schauder Fixed Point Theorem. Communications in Advanced Mathematical Sciences. Mart 2021;4(1):39-45. doi:10.33434/cams.860254
Chicago Temizer Ersoy, Merve. “Numerical Solution of a Quadratic Integral Equation through Classical Schauder Fixed Point Theorem”. Communications in Advanced Mathematical Sciences 4, sy. 1 (Mart 2021): 39-45. https://doi.org/10.33434/cams.860254.
EndNote Temizer Ersoy M (01 Mart 2021) Numerical Solution of a Quadratic Integral Equation through Classical Schauder Fixed Point Theorem. Communications in Advanced Mathematical Sciences 4 1 39–45.
IEEE M. Temizer Ersoy, “Numerical Solution of a Quadratic Integral Equation through Classical Schauder Fixed Point Theorem”, Communications in Advanced Mathematical Sciences, c. 4, sy. 1, ss. 39–45, 2021, doi: 10.33434/cams.860254.
ISNAD Temizer Ersoy, Merve. “Numerical Solution of a Quadratic Integral Equation through Classical Schauder Fixed Point Theorem”. Communications in Advanced Mathematical Sciences 4/1 (Mart 2021), 39-45. https://doi.org/10.33434/cams.860254.
JAMA Temizer Ersoy M. Numerical Solution of a Quadratic Integral Equation through Classical Schauder Fixed Point Theorem. Communications in Advanced Mathematical Sciences. 2021;4:39–45.
MLA Temizer Ersoy, Merve. “Numerical Solution of a Quadratic Integral Equation through Classical Schauder Fixed Point Theorem”. Communications in Advanced Mathematical Sciences, c. 4, sy. 1, 2021, ss. 39-45, doi:10.33434/cams.860254.
Vancouver Temizer Ersoy M. Numerical Solution of a Quadratic Integral Equation through Classical Schauder Fixed Point Theorem. Communications in Advanced Mathematical Sciences. 2021;4(1):39-45.

Cited By

On the Solvability of a Class of Nonlinear Integral Equations in Hölder Spaces
Numerical Functional Analysis and Optimization
https://doi.org/10.1080/01630563.2022.2032148

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