W-distance based ϕ-coupled fixed point problem: Solution, well-posedness and applications to integral and functional equations

References

[1] C. Alegre Gil, E. Karapınar, J. Marín Molina and P. Tirado Peláez, Revisiting Bianchini and Grandolfi theorem in the context of modified ω-distances, Results Math. 74 (2019), no. 4, Paper No. 149. 10.1007/s00025-019-1074-zSuche in Google Scholar

[2] M. Asadi, Discontinuity of control function in the ( F , φ , θ ) -contraction in metric spaces, Filomat 31 (2017), no. 17, 5427–5433. 10.2298/FIL1717427ASuche in Google Scholar

[3] H. Aydi, T. Wongyat and W. Sintunavarat, On new evolution of Ri’s result via w-distances and the study on the solution for nonlinear integral equations and fractional differential equations, Adv. Difference Equ. 2018 (2018), Paper No. 132. 10.1186/s13662-018-1590-2Suche in Google Scholar

[4] B. S. Choudhury and P. Chakraborty, Fixed point problem of a multi-valued Kannan–Geraghty type contraction via w-distance, J. Anal. 31 (2023), no. 1, 439–458. 10.1007/s41478-022-00457-3Suche in Google Scholar

[5] B. S. Choudhury and A. Kundu, A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal. 73 (2010), no. 8, 2524–2531. 10.1016/j.na.2010.06.025Suche in Google Scholar

[6] B. S. Choudhury, N. Metiya and S. Kundu, Existence, data-dependence and stability of coupled fixed point sets of some multivalued operators, Chaos Solitons Fractals 133 (2020), Article ID 109678. 10.1016/j.chaos.2020.109678Suche in Google Scholar

[7] Y. Fan, C. Zhu and Z. Wu, Some φ-coupled fixed point results via modified F-control function’s concept in metric spaces and its applications, J. Comput. Appl. Math. 349 (2019), 70–81. 10.1016/j.cam.2018.09.013Suche in Google Scholar

[8] H. Garai, H. K. Nashine, L. K. Dey and R. W. Ibrahim, Fixed point results via modified ω-distance and an application to networks communication, Filomat 36 (2022), no. 12, 4123–4137. 10.2298/FIL2212123GSuche in Google Scholar

[9] T. Gnana Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), no. 7, 1379–1393. 10.1016/j.na.2005.10.017Suche in Google Scholar

[10] D. J. Guo and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal. 11 (1987), no. 5, 623–632. 10.1016/0362-546X(87)90077-0Suche in Google Scholar

[11] M. Jleli, B. Samet and C. Vetro, Fixed point theory in partial metric spaces via φ-fixed point’s concept in metric spaces, J. Inequal. Appl. 2014 (2014), Article ID 426. 10.1186/1029-242X-2014-426Suche in Google Scholar

[12] O. Kada, T. Suzuki and W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon. 44 (1996), no. 2, 381–391. Suche in Google Scholar

[13] E. Karapinar, A. Abbas and S. Farooq, A discussion on the existence of best proximity points that belong to the zero set, Axioms 9 (2020), 10.3390/axioms9010019. 10.3390/axioms9010019Suche in Google Scholar

[14] E. Karapinar, S. Romaguera and P. Tirado, Characterizations of quasi-metric and G-metric completeness involving w-distances and fixed points, Demonstr. Math. 55 (2022), no. 1, 939–951. 10.1515/dema-2022-0177Suche in Google Scholar

[15] P. Kumrod and W. Sintunavarat, A new contractive condition approach to φ-fixed point results in metric spaces and its applications, J. Comput. Appl. Math. 311 (2017), 194–204. 10.1016/j.cam.2016.07.016Suche in Google Scholar

[16] V. Lakshmikantham and L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009), no. 12, 4341–4349. 10.1016/j.na.2008.09.020Suche in Google Scholar

[17] H. Lakzian, D. Gopal and W. Sintunavarat, New fixed point results for mappings of contractive type with an application to nonlinear fractional differential equations, J. Fixed Point Theory Appl. 18 (2016), no. 2, 251–266. 10.1007/s11784-015-0275-7Suche in Google Scholar

[18] H. Lakzian, V. Rakočević and H. Aydi, Extensions of Kannan contraction via w-distances, Aequationes Math. 93 (2019), no. 6, 1231–1244. 10.1007/s00010-019-00673-6Suche in Google Scholar

[19] H. Lakzian and B. E. Rhoades, Some fixed point theorems using weaker Meir–Keeler function in metric spaces with w-distance, Appl. Math. Comput. 342 (2019), 18–25. 10.1016/j.amc.2018.06.048Suche in Google Scholar

[20] Z. Liu, Y. Lu and S. M. Kang, Fixed point theorems for multi-valued contractions with w-distance, Appl. Math. Comput. 224 (2013), 535–552. 10.1016/j.amc.2013.08.061Suche in Google Scholar

[21] V. Rakočević, Fixed Point Results in W-Distance Spaces, Monogr. Res. Notes Math., CRC Press, Boca Raton, 2021. 10.1201/9781003213444Suche in Google Scholar

[22] S. Roy, P. Chakraborty, S. Ghosh, P. Saha and B. S. Choudhury, Investigation of a fixed point problem for pata-type contractions with respect to w-distance, J. Anal. 32 (2024), no. 1, 125–136. 10.1007/s41478-023-00612-4Suche in Google Scholar

[23] S. Roy, P. Saha and B. S. Choudhury, Extensions of φ-fixed point results via w-distance, Sahand Commun. Math. Anal. 21 (2024), no. 2, 219–234. Suche in Google Scholar

[24] H. N. Saleh, M. Imdad and E. Karapinar, A study of common fixed points that belong to zeros of a certain given function with applications, Nonlinear Anal. Model. Control 26 (2021), no. 5, 781–800. 10.15388/namc.2021.26.21945Suche in Google Scholar

[25] Y. Sun, X.-l. Liu, J. Deng, M. Zhou and H. Zhang, Some new φ-fixed point and φ-fixed disc results via auxiliary functions, J. Inequal. Appl. 2022 (2022), Paper No. 116. 10.1186/s13660-022-02852-7Suche in Google Scholar

[26] T. Wongyat and W. Sintunavarat, The existence and uniqueness of the solution for nonlinear Fredholm and Volterra integral equations together with nonlinear fractional differential equations via w-distances, Adv. Difference Equ. 2017 (2017), Paper No. 211. 10.1186/s13662-017-1267-2Suche in Google Scholar