Coupled fixed point results in ordered partial metric spaces and application to the Volterra type integral equations
Keywords:
coupled fixed point, contractive type condition, partial metric space, partially ordered set, control functionAbstract
The goal of this study is to demonstrate coupled fixed point theorems for contractive type conditions with control functions in partially ordered partial metric spaces. Furthermore, some consequences of the established conclusions are discussed, as well as illustrative instances to back up the findings. An application to the Volterra type integral equation is also shown, followed by an illustration.
References
[1] T. Abdeljawad, H. Aydi, E. Karapinar, Coupled fixed points for Meir-Keeler contractions in ordered partial metric spaces, Mathematical Problems in Engineering 2012(1) 327273.
[2] H. Aydi, Some coupled fixed point results on partial metric spaces, International J. Math. Math. Sci. 2011, Article ID 647091, 11 pages.
[3] H. Aydi, M. Abbas, C. Vetro, Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces, Topology and Its Appl. 159(14) (2012) 3234–3242.
[4] S. Banach, Surles operation dans les ensembles abstraits et leur application aux equation integrals, Fund. Math. 3 (1922) 133–181.
[5] T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis: TMA 65(7) (2006) 1379–1393.
[6] N. Bilgili, I. M. Earhan, E. Karapinar and D. Turkoglu, A note coupled fixed point theorems for mixed g-monotone mappings in partially ordered metric spaces, Fixed Point Theory Appl. (2014) 1–6.
[7] L. Ciric, V. Lakshmikantham, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis: TMA 70(12) (2009) 4341–4349.
[8] S. Chandok, D. Kumar, M. S. Khan, Some results in partial metric space using auxiliary functions, Applied Math. E-Notes 15 (2015) 233–242.
[9] D. Guo and V. Lakshmikantham, Coupled fixed point of nonlinear operator with application, Nonlinear Anal. TMA. 11 (1987) 623–632.
[10] R. Heckmann, Approximation of metric spaces by partial metric spaces, Appl. Categ. Structures 7(1-2) (1999) 71–83.
[11] E. Karapınar, I. M. Erhan, Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett. 24(11) (2011) 1900–1904.
[12] E. Karapinar, N. V. Luong, N. X. Thuan, Coupled coincidence points for mixed monotone opertors in partially ordered metric spaces, Arabian J. Math. 1 (2012) 329–339.
[13] E. Karapinar, W. Shatanawi, K. Tas, Fixed point theorems on partial metric spaces involving rational expressions, Miskolc Math. Notes 14 (2013) 135–142.
[14] E. Karapinar, R. P. Agarwal, Fixed Point Theory in Generalized Metric Spaces, Springer 2022.
[15] H. P. A. K¨unzi, H. Pajoohesh, M. P. Schellekens, Partial quasi-metrics, Theoritical Comput. Sci. 365(3) (2006) 237–246.
[16] D. Kumar, S. Sadat, J. R. Lee, C. Park, Some theorems in partial metric spaces using auxiliary functions, AIMS Maths. 6(7) (2021) 6734–6748.
[17] S. G. Matthews, Partial metric topology, Research report 2012, Dept. Computer Science, University of Warwick, 1992.
[18] S. G. Matthews, Partial metric topology, Proceedings of the 8th summer conference on topology and its applications, Annals of the New York Academy of Sciences 728(1994) 183–197.
[19] H. K. Nashine , G.S. Saluja, G. V. V. J. Rao, W. H. Lim, Control function based coupled and common coupled fixed point theorems in partial metric spaces, Nonlinear Functional Anal. Appl. 29(2) (2024) 559–580.
[20] V. Popa, A. M. Patriciu, Fixed point theorems for two pairs of mappings in partial metric spaces, Facta Univ. (NIS), Ser. Math. Inform. 31(5) (2016) 969–980.
[21] S. Radenovi´c, Some coupled coincidence points results of monotone mappings in partially ordered metric spaces, Int. J. Anal. Appl. 5(2) (2014) 174–184.
[22] A. Roldan, J. Moreno-Martinez, C. Roldan, E. Karapinar, Multidimensional fixed point theorems in partially ordered complete partial metric spaces under (ψ, φ)-contractivity conditions, Abstr. Appl. Anal. (2013) 2013: 634371.
[23] G. S. Saluja, Results for coupled fixed point in partial metric spaces via contractive type condition involving rational term, J. Indian Math. Soc. 91(3-4) (2024), 426–445.
[24] B. Samet, M. Rajovi´c, R. Lazovi´c, R. Stoiljkovi´c, Common fixed point results for nonlinear contractions in ordered partial metric spaces, Fixed Point Theory Appl. (2011) 2011:71.
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