SOLUTION OF CERTAIN PERIODIC BOUNDARY VALUE PROBLEM IN RELATIONAL METRIC SPACE VIA RELATIONAL ALMOST <i>φ</i>-CONTRACTIONS

Doaa Filali; Nidal H. E. Eljaneid; Amal F. Alharbi; Esmail Alshaban; Faizan Ahmad Khan; Mohammed Zayed Alruwaytie

doi:10.11948/20240195

2025 Volume 15 Issue 3

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2025 > 15(3): 1272-1283

Next Article Previous Article

Doaa Filali, Nidal H. E. Eljaneid, Amal F. Alharbi, Esmail Alshaban, Faizan Ahmad Khan, Mohammed Zayed Alruwaytie. SOLUTION OF CERTAIN PERIODIC BOUNDARY VALUE PROBLEM IN RELATIONAL METRIC SPACE VIA RELATIONAL ALMOST φ-CONTRACTIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1272-1283. doi: 10.11948/20240195

Citation:

Doaa Filali, Nidal H. E. Eljaneid, Amal F. Alharbi, Esmail Alshaban, Faizan Ahmad Khan, Mohammed Zayed Alruwaytie. SOLUTION OF CERTAIN PERIODIC BOUNDARY VALUE PROBLEM IN RELATIONAL METRIC SPACE VIA RELATIONAL ALMOST φ-CONTRACTIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1272-1283. doi: 10.11948/20240195

SOLUTION OF CERTAIN PERIODIC BOUNDARY VALUE PROBLEM IN RELATIONAL METRIC SPACE VIA RELATIONAL ALMOST φ-CONTRACTIONS

1.
Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, Riyadh-11671, Saudi Arabia
2.
Department of Mathematics, University of Tabuk, Tabuk-71491, Saudi Arabia
3.
Department of Mathematics, King Abdulaziz University, Jeddah-21589, Saudi Arabia
4.
Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyad-11673, Saudi Arabia

Author Bio: Email: dkfilali@pnu.edu.sa(D. Filali); Email: neljaneid@ut.edu.sa(N. H. E. Eljaneid); Email: afsalharbe@kau.edu.sa(A. F. Alharbi); Email: ealshaban@ut.edu.sa(E. Alshaban); Email: m.alruwaytie@seu.edu.sa(M. Z. Alruwaytie)
Corresponding author: Email: fkhan@ut.edu.sa(F. A. Khan)
Fund Project: The first author was supported by Princess Nourah bint Abdulrahman University Researchers project number (PNURSP2025R174)

Abstract

Abstract

This article is comprised of outcomes on fixed points for almost Matkowski contractions via locally $\mathcal{J} $-transitive relations. Our outcomes sharpen, unify, enrich and improve many fixed point theorems of the existing literatures. Several examples are furnished to demonstrate the credibility of our results. By implementing our outcomes, we ascertain a unique solution for certain boundary value problem.
- Fixed points /
- binary relations /
- almost contractions /
- boundary value problems
MSC: 47H10, 54H25, 06A75, 34B15

FullText(HTML)

References

[1]	R. P. Agarwal, M. A. El-Gebeily and D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., 2008, 87(1), 109–116. doi: 10.1080/00036810701556151 CrossRef Google Scholar
[2]	A. Alam, M. Arif and M. Imdad, Metrical fixed point theorems via locally finitely T-transitive binary relations under certain control functions, Miskolc Math. Notes, 2019, 20(1), 59–73. doi: 10.18514/MMN.2019.2468 CrossRef Google Scholar
[3]	A. Alam, R. George and M. Imdad, Refinements to relation-theoretic contraction principle, Axioms, 2022, 11, 316, 6 pp. Google Scholar
[4]	A. Alam and M. Imdad, Relation-theoretic contraction principle, J. Fixed Point Theory Appl., 2015, 17(4), 693–702. doi: 10.1007/s11784-015-0247-y CrossRef Google Scholar
[5]	A. Alam and M. Imdad, Relation-theoretic metrical coincidence theorems, Filomat, 2017, 31(14), 4421–4439. doi: 10.2298/FIL1714421A CrossRef Google Scholar
[6]	A. Alam and M. Imdad, Nonlinear contractions in metric spaces under locally T-transitive binary relations, Fixed Point Theory, 2018, 19(1), 13–24. Google Scholar
[7]	S. F. Aldosary, I. Uddin and S. Mujahid, Relational Geraghty contractions with an application to a singular fractional boundary value problem, J. Appl. Anal. Comp., 2024, 14(6), 3480–3495. Google Scholar
[8]	B. Almarri, S. Mujahid and I. Uddin, New fixed point results for Geraghty contractions and their applications, J. Appl. Anal. Comp., 2023, 13(5), 2788–2798. Google Scholar
[9]	N. H. Altaweel and F. A. Khan, Relation-theoretic fixed point theorems involving certain auxiliary functions with applications, Symmetry, 2022, 14, 2614, 12 pp. Google Scholar
[10]	M. Arif, M. Imdad and A. Alam, Fixed point theorems under locally T-transitive binary relations employing Matkowski contractions, Miskolc Math. Notes, 2022, 23(1), 71–83. doi: 10.18514/MMN.2022.3220 CrossRef Google Scholar
[11]	M. Arif, I. A. Khan, M. Imdad and A. Alam, Employing locally finitely T-transitive binary relations to prove coincidence theorems for nonlinear contractions, J. Funct. Spaces, 2020, 2020, 6574695, 12 pp. Google Scholar
[12]	V. Berinde, Iterative Approximation of Fixed Points, Springer-Verlag, Heidelberg, Germany, 2007. Google Scholar
[13]	V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum., 2004, 9(1), 43–53. Google Scholar
[14]	N. H. E. Eljaneid, F. A. Khan, H. I. A. Mohammed and A. Alam, Relational quasi-contractions and related fixed point theorems, J. Math., 2022, 2022, 4477660, 6 pp. Google Scholar
[15]	A. Hossain, F. A. Khan and Q. H. Khan, A relation-theoretic metrical fixed point theorem for rational type contraction mapping with an application, Axioms, 2021, 10, 316, 11 pp. Google Scholar
[16]	F. A. Khan, Almost contractions under binary relations, Axioms, 2022, 11, 441, 7 pp. Google Scholar
[17]	F. A. Khan, F. Sk, M. G. Alshehri, Q. H. Khan and A. Alam, Relational Meir-Keeler contractions and common fixed point theorems, J. Funct. Spaces, 2022, 2022, 3550923, 9 pp. Google Scholar
[18]	J. Matkowski, Integrable solutions of functional equations, Dissertationes Math., 1975, 127, 68 pp. Google Scholar
[19]	J. J. Nieto and R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order., 2005, 22(3), 223–239. doi: 10.1007/s11083-005-9018-5 CrossRef Google Scholar
[20]	D. O'Regan and A. Petruşel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., 2008, 341(2), 1241–1252. doi: 10.1016/j.jmaa.2007.11.026 CrossRef Google Scholar
[21]	M. Pǎcurar, Remark regarding two classes of almost contractions with unique fixed point, Creative Math. Inf., 2010, 19(2), 178–183. Google Scholar
[22]	B. Samet and M. Turinici, Fixed point theorems on a metric space endowed with an arbitrary binary relation and applications, Commun. Math. Anal., 2012, 13(2), 82–97. Google Scholar
[23]	F. Sk, F. A. Khan, Q. H. Khan and A. Alam, Relation-preserving generalized nonlinear contractions and related fixed point theorems, AIMS Math., 2022, 7(4), 6634–6649. Google Scholar