Best proximity points in ℱ-metric spaces with applications

• Autorzy: Lateef Durdana

Identyfikatory

DOI

10.1515/dema-2022-0191

• Języki publikacji: EN

Abstrakty

EN

The aim of this article is to introduce α - ψ -proximal contraction in the setting of ℱ-metric space and prove the existence of best proximity points for these contractions. As applications of our main results, we obtain coupled best proximity points on ℱ-metric space equipped with an arbitrary binary relation.

Słowa kluczowe

EN

best proximity point; α-ψ-proximal contraction; non-self mappings; coupled best proximity point

PL

punkty najlepszej bliskości; odwzorowania; przestrzenie metryczne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20220191
• Opis fizyczny: Bibliogr. 35 poz.

Twórcy

autor

Lateef Durdana

• Department of Mathematics, College of Science, Taibah University, Al Madina Al Munawwara, Madina 41411, Saudi Arabia

Bibliografia

• [1] S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrales, Fundam. Math. 3 (1922), 133–181.
• [2] S. S. Basha, Extensions of Banachas contraction principle, Numer. Funct. Anal. Optim. 31 (2010), 569–576.
• [3] A. Eldred and P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl. 323 (2006), no. 2, 1001–1006.
• [4] B. Samet, C. Vetro, and P. Vetro, Fixed point theorem for α-ψ-contractive type mappings, Nonlinear Anal. 75 (2012), 2154–2165.
• [5] M. Jleli and B. Samet, Best proximity points for (α-ψ)-proximal contractive type mappings and applications, Bulletin des Sciences Mathematiques 137 (2013), 977–995.
• [6] A. Abkar and M. Gabeleh, Best proximity points for cyclic mappings in ordered metric spaces, J. Optim. Theory Appl. 150 (2011), 188–193.
• [7] A. Abkar and M. Gabeleh, The existence of best proximity points for multivalued non-self-mappings, Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM 107 (2013), 319–325.
• [8] G. Gecheva, M. Hristov, D. Nedelcheva, M. Ruseva, and B. Zlatanov, Applications of coupled fixed points for multivalued maps in the equilibrium in duopoly markets and in aquatic ecosystems, Axioms 10 (2021), no. 2, 44, DOI: https://doi.org/10.3390/axioms10020044.
• [9] M. Hristov, A. Ilchev, and B. Zlatanov, On some application on coupled and best proximity points theorems, In:AIP Confer. Proc. 2333 (2021), 080008, DOI: https://doi.org/10.1063/5.0041716.
• [10] M. Hristov, A. Ilchev, and B. Zlatanov, Coupled fixed points for Chatterjea type maps with the mixed monotone property in partially ordered metric spaces, AIP Confer. Proc. 2172 (2019), 060003, DOI: https://doi.org/10.1063/1.5133531.
• [11] B. Zlatanov. Best proximity points in modular function spaces, Arabian J. Math. 4 (2015), no. 3, 215–227
• [12] A. Ilchev and B. Zlatanov. Fixed and best proximity points forKannan cyclic contractions in modular function spaces, J. Fixed Point Theory Appl. 19 (2017), no. 4, 2873–2893.
• [13] A. Ilchev and B. Zlatanov, Coupled fixed points and coupled best proximity points in modular function spaces, Int. J. Pure Appl. Math. 118 (2018), no. 4, 957–977.
• [14] A. Ilchev and B. Zlatanov. Coupled fixed points and coupled best proximity points for cyclic Kannan type contraction maps in modular function spaces, Mattex Confer. Proc. 1 (2018), 75–88.
• [15] B. Zlatanov, Coupled best proximity points for cyclic contractive maps and their applications, Fixed Point Theory 22 (2021), 431–452.
• [16] I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal. 30 (1989), 26–37.
• [17] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostra. 1 (1993), 5–11.
• [18] M. Jleli and B. Samet, On a new generalization of Metric Spaces, J. Fixed Point Theory Appl. 20 (2018), 128.
• [19] S. A. Al-Mezel, J. Ahmad, and G. Marino, Fixed point theorems for generalized (αβ-ψ)-Contractions in -metric spaces with applications, Mathematics 8 (2020), no. 4, 584, DOI: https://doi.org/10.3390/math8040584.
• [20] J. Ahmad, A. S. Al-Rawashdeh, and A. E. Al-Mazrooei, Fixed point results for ( ⊥α, )-contractions in orthogonal -metric spaces with applications, J. Funct. Spaces 2022 (2022), no. 3, 1–10.
• [21] M. Alansari, S. Mohammed, and A. Azam, Fuzzy fixed point results in -metric spaces with applications, J. Function Spaces. 2020 (2020), 5142815, 11 pages.
• [22] A. E. Al-Mazrooei and J. Ahmad, Fixed point theorems for rational contractions in -metric spaces, J. Math. Anal. 10 (2019), 79–86.
• [23] L. A. Alnaser, D. Lateef, H. A. Fouad, and J. Ahmad, Relation theoretic contraction results in -metric spaces, J. Nonlinear Sci. Appl. 12 (2019), 337–344.
• [24] L. A. Alnaser, D. Lateef, H. A. Fouad, and J. Ahmad, New fixed point theorems with applications to non-linear neutral differential equations, Symmetry 11 (2019), 602.
• [25] O. Alqahtani, E. Karapiiinar, and P. Shahi, Common fixed point results in function weighted metric spaces. J. Inequal. Appl. 2019 (2019), 164.
• [26] A. Beraž, H. Garai, B. Damjanović, and A. Chanda, Some interesting results on -metric spaces, Filomat 33 (2019), no. 10, 3257–3268.
• [27] D. Lateef and D. J. Ahmad, Dass and Guptaas Fixed point theorem in F -metric spaces, J. Nonlinear Sci. Appl. 12 (2019), 405–411.
• [28] A Hussain, H Al-Sulami, N Hussain, and H. Farooq, Newly fixed disc results using advanced contractions on -metric space, J. Appl. Anal. Comput. 10 (2020), no. 6, 2313–2322.
• [29] F. Jahangir, P. Haghmaram, and K. Nourouzi, A note on F -metric spaces, J. Fixed Point Theory Appl. 23 (2021), 2.
• [30] T. Kanwal, A. Hussain, H. Baghani, and M. de la Sen, New fixed point theorems in orthogonal -metric spaces with application to fractional differential equation, Symmetry 12 (2020), no. 5, 832.
• [31] Z. D. Mitrović, H. Aydi, N. Hussain, and A. Mukheimer, Reich, Jungck, and Berinde common fixed point results on -metric spaces and an application, Mathematics. 7 (2019), no. 5, 387.
• [32] A. Tomar and M. Joshi, Relation-theoretic nonlinear contractions in an -metric space and applications, Rendiconti del Circolo Matematico di Palermo Series 70 (2021), 835–852.
• [33] C. Zhu, J. Chen, J. Chen, C. Chen, and H. Huang, A new generalization of -metric spaces and some fixed point theorems and applications, J. Appl. Anal. Comput. 11 (2021), 2649–2663.
• [34] D. Guo and V. Lakshmikantham, Coupled fixed points of nonlinear operators with application, Nonlinear Anal. 11 (1987), no. 5, 623–632.
• [35] T. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), no. 7, 1379–1393.