Existence and Uniqueness of Solutions to Third-Order Boundary Value Problems

The purpose of this research is to connect fixed point methods with certain third-order boundary value problems in new and interesting ways. Our strategy involves an analysis of the problem under consideration within closed and bounded sets. We develop sufficient conditions under which the associated mappings will be contractive and invariant in these sets, which generates new advances concerning the existence, uniqueness and approximation of solutions.

Keywords:
third-order boundary value problem; existence; uniqueness and approximation of solutions; contraction mappings; fixed point theorems; closed and bounded sets; two and three-point boundary conditions

Authorship

S. S. ALMUTHAYBIRI

School of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, AustraliaThe University of New South WalesAustraliaAustraliaSchool of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia

Department of Mathematics, College of Science and Arts in Uglat Asugour, Qassim University, Buraydah, Kingdom of Saudi Arabia - E-mail: s.almuthaybiri@qu.edu.saQassim UniversityKingdom of Saudi ArabiaBuraydah, Kingdom of Saudi ArabiaDepartment of Mathematics, College of Science and Arts in Uglat Asugour, Qassim University, Buraydah, Kingdom of Saudi Arabia - E-mail: s.almuthaybiri@qu.edu.sa

https://orcid.org/0000-0002-9399-3253

J. M. JONNALAGADDA

Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad, 500078, Telangana, India - E-mail: j.jaganmohan@hotmail.comBirla Institute of Technology and Science PilaniIndiaHyderabad, Telangana, IndiaDepartment of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad, 500078, Telangana, India - E-mail: j.jaganmohan@hotmail.com

https://orcid.org/0000-0002-1310-8323

C. C. TISDELL ^**Corresponding author: Christopher C. Tisdell - E-mail: cct@unsw.edu.au

School of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia - E-mail: cct@unsw.edu.auThe University of New South WalesAustraliaSydney, New South Wales, AustraliaSchool of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia - E-mail: cct@unsw.edu.au

https://orcid.org/0000-0002-3387-2505

^*Corresponding author: Christopher C. Tisdell - E-mail: cct@unsw.edu.au

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