Skip to main content
Springer Nature Link
Log in

Solution of infinite system of third-order three-point nonhomogeneous boundary value problem in weighted sequence space \({{\varvec{bv}}}_{{{\varvec{p}}}}^{\omega }\)

  • Published:
Rendiconti del Circolo Matematico di Palermo Series 2 Aims and scope Submit manuscript

Abstract

We introduce the concept of weighted sequence space \(bv_p^\omega \) and we construct a Hausdorff measure of noncompactness (MNC) in this space. Then, by applying this MNC we study the existence of solutions of infinite systems of third-order three-point nonhomogeneous boundary value problem in \(bv_p^{\omega }\). Finally, we present two examples to show the usefulness of our results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Data availibility

The manuscript has no associated data.

References

  1. Aghajani, A., Banaś, J., Jalilian, Y.: Existence of solution for a class of nonlinear Volterra singular integral equation. Comput. Math. Appl. 62, 1215–1227 (2011)

    Article  MathSciNet  Google Scholar 

  2. Aghajani, A., Mursaleen, M., Shole Haghighi, A.: Fixed point theorems for Meir-Keeler condensing operators via measure of noncompactness. Acta Math. Sci. 35B, 552–566 (2015)

    Article  MathSciNet  Google Scholar 

  3. Aghajani, A., Pourhadi, E.: Application of measure of noncompactness to \(l_1\)-solvability of infinite systems of second order differential equations. Bull. Belg. Math. Soc. Simon Stevin 22(1), 105–118 (2015)

    Article  MathSciNet  Google Scholar 

  4. Alotaibi, A., Mursaleen, M., Alamri, B.A.S.: Solvability of second order linear differential equations in the sequence space \(n(\phi )\). Adv. Differ. Equ. 2018, 377 (2018)

    Article  MathSciNet  Google Scholar 

  5. Anderson, D.: Green’s function for a third-order generalized right focal problem. J. Math. Anal. Appl. 288, 1–14 (2003)

    Article  MathSciNet  Google Scholar 

  6. Anderson, D.: Multiple positive solutions for a three-point boundary value problem. Math. Comput. Model. 27, 49–57 (1998)

    Article  MathSciNet  Google Scholar 

  7. Anderson, D., Davis, J.M.: Multiple solutions and eigenvalues for third-order right focal boundary value problems. J. Math. Anal. Appl. 267, 135–157 (2002)

    Article  MathSciNet  Google Scholar 

  8. Bai, Z., Fei, X.: Existence of triple positive solutions for a third order generalized right focal problem. Math. Inequal. Appl. 9, 437–444 (2006)

    MathSciNet  Google Scholar 

  9. Banaś, J., Goebel, K.: Measures of Noncompactness in Banach Spaces. Lecture Notes in Pure and Applied Mathematics, vol. 60. Marcel Dekker, New York (1980)

    Google Scholar 

  10. Banaś, J., Lecko, M.: Solvability of infinite systems of differential equations in Banach sequence spaces. J. Comput. Appl. Math. 137, 363–375 (2001)

    Article  MathSciNet  Google Scholar 

  11. Banaś, J., Mursaleen, M.: Sequence Spaces and Measure of Noncompactness with Applications to Differential and Integral Equation. Springer, New Delhi (2014)

    Book  Google Scholar 

  12. Banaś, J., Mursaleen, M., Rizvi, S.M.H.: Existence of solutions to a boundary-value problem for an infinite system of differential equations. Electron. J. Differ. Equ. 262, 12 (2017)

    MathSciNet  Google Scholar 

  13. Basar, F.: Summability Theory and its Appliactions. Bentham Science Publishers, Sharjah (2011)

    Google Scholar 

  14. Basar, F., Altay, B.: On the space of sequences of \(p-\)bounded variation and related matrix mappings. Ukr. Math. J. 55, 136–147 (2003)

    Article  MathSciNet  Google Scholar 

  15. Bellman, R.: Methods of Nonlinear Analysis, vol. II. Academic Press, New York (1973)

    Google Scholar 

  16. Boucherif, A., Al-Malki, N.: Nonlinear three-point third order boundary value problems. Appl. Math. Comput. 190, 1168–1177 (2007)

    MathSciNet  Google Scholar 

  17. Deimling, K.: Ordinary Differential Equations in Banach Spaces. Lecture Notes in Mathematics, vol. 596. Springer, Berlin (1977)

    Google Scholar 

  18. Graef, J.R., Yang, B.: Multiple positive solutions to a three point third order boundary value problem. Discrete Contin. Dyn. Syst. (Suppl.), 1–8 (2005)

  19. Gregus, M.: Third Order Linear Differential Equations. Mathematics and its Applications, Reidel, Dordrecht (1987)

    Book  Google Scholar 

  20. Grossinho, M.R., Minhos, F.M.: Existence result for some third order separated boundary value problems. Nonlinear Anal. 47, 2407–2418 (2001)

    Article  MathSciNet  Google Scholar 

  21. Hazarika, B., Das, A., Arab, R., Mursaleen, M.: Solvability of the infinite system of integral equations in two variables in the sequence spaces \(c_0\) and \(l_1\). J. Comput. Appl. Math. 326, 183–192 (2012)

    Google Scholar 

  22. Jarrah, A.M., Malkowsky, E.: Ordinary, absolute and strong summability and matrix transformations. Filomat 17, 59–78 (2003)

    Article  MathSciNet  Google Scholar 

  23. Kuratowski, K.: Sur les espaces complets. Fund. Math. 15, 301–309 (1930)

    Article  Google Scholar 

  24. Meir, A., Keeler, E.A.: Theorem on contraction mappings. J. Math. Anal. Appl. 28, 326–329 (1969)

    Article  MathSciNet  Google Scholar 

  25. Mursaleen, M.: Application of measure of noncompactness to infinite system of differential equations. Canad. Math. Bull. 56, 388–394 (2013)

    Article  MathSciNet  Google Scholar 

  26. Mursaleen, M.: Some geometric properties of a sequence space related to \(l_p\). Bull. Aust. Math. Soc. 67(2), 343–347 (2003)

    Article  Google Scholar 

  27. Mursaleen, M., Bilalov, B., Rizvi, S.M.H.: Applications of measures of noncompactness to infinite system of fractional differential equations. Filomat 31(11), 3421–3432 (2017)

    Article  MathSciNet  Google Scholar 

  28. Mursaleen, M., Mohiuddine, S.A.: Applications of measures of noncompactness to the infinite system of differential equations in \(l_p\) spaces. Nonlinear Anal. 75, 2111–2115 (2012)

    Article  MathSciNet  Google Scholar 

  29. Mursaleen, M., Rizvi, S.M.H.: Solvability of infinite system of second order differential equations in \(c_0\) and \(l_1\) by Meir-Keeler condensing operator. Proc. Am. Math. Soc. 144(10), 4279–4289 (2016)

    Article  Google Scholar 

  30. Oguzt Poreli, M.N.: On the neural equations of Cowan and Stein. Util. Math. 2, 305–315 (1972)

    MathSciNet  Google Scholar 

  31. Pouhadi, E., Mursaleen, M., R, S.: On a class of infinite system of third-order differential equations in \(l_{p}\) via measure of noncompactness. Filomat 34(11), 3861–3870 (2020)

    Article  MathSciNet  Google Scholar 

  32. Saadati, R., Pourhadi, E., Mursaleen, M.: Solvability of infinite systems of third-order differential equations in \(c_0\) by Meir-Keeler condensing operators. J. Fixed Point Theory Appl. 21(2), 1–16 (2019)

    Article  Google Scholar 

  33. Sun, Y.: Positive solutions for third-order three-point nonhomogeneous boundary value problems. Appl. Math. Lett. 22, 45–51 (2009)

    Article  MathSciNet  Google Scholar 

  34. Sun, Y.: Positive solutions of singular third-order three-point boundary value problems. J. Math. Anal. Appl. 306, 589–603 (2005)

    Article  MathSciNet  Google Scholar 

  35. Yao, Q.: The existence and multiplicity of positive solutions for a third-order three-point boundary value problem. Acta Math. Appl. Sin. 19, 117–122 (2003)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

    H. Amiri Kayvanloo & M. Khanehgir

  2. Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan

    M. Mursaleen

  3. University Centre for Research and Development, Chandigarh University, Mohali, 140243, Punjab, India

    M. Mursaleen

Authors
  1. H. Amiri Kayvanloo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Khanehgir
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Mursaleen
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All the authors contributed equally and significantly in writing this paper.

Corresponding author

Correspondence to M. Mursaleen.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Amiri Kayvanloo, H., Khanehgir, M. & Mursaleen, M. Solution of infinite system of third-order three-point nonhomogeneous boundary value problem in weighted sequence space \({{\varvec{bv}}}_{{{\varvec{p}}}}^{\omega }\). Rend. Circ. Mat. Palermo, II. Ser 73, 1329–1342 (2024). https://doi.org/10.1007/s12215-023-00986-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12215-023-00986-1

Keywords

Mathematics Subject Classification

Search

Navigation