Interpolative Reich-Rus-Ciric and Hardy-Rogers Contraction on Quasi-Partial b-Metric Space and Related Fixed Point Results

[EN] The aim of this paper was to obtain common fixed point results by using an interpolative contraction condition given by Karapinar in the setting of complete metric space. Here in this paper, we have redefined the Reich-Rus-Ciric type contraction and Hardy-Rogers type contraction in the framework of quasi-partial b-metric space and proved the corresponding common fixed point theorem by adopting the notion of interpolation. The results are further validated with the application based on them.Mishra, VN.; Sánchez Ruiz, LM.; Gautam, P.; Verma, S. (2020). Interpolative Reich-Rus-Ciric and Hardy-Rogers Contraction on Quasi-Partial b-Metric Space and Related Fixed Point Results. Mathematics. 8(9):1-11. https://doi.org/10.3390/math8091598S11189Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta Mathematicae, 3, 133-181. doi:10.4064/fm-3-1-133-181Shukla, S. (2013). Partial b-Metric Spaces and Fixed Point Theorems. Mediterranean Journal of Mathematics, 11(2), 703-711. doi:10.1007/s00009-013-0327-4MATTHEWS, S. G. (1994). Partial Metric Topology. Annals of the New York Academy of Sciences, 728(1 General Topol), 183-197. doi:10.1111/j.1749-6632.1994.tb44144.xKARAPINAR, E. (2018). Revisiting the Kannan Type Contractions via Interpolation. Advances in the Theory of Nonlinear Analysis and its Application, 85-87. doi:10.31197/atnaa.431135Reich, S. (1971). Some Remarks Concerning Contraction Mappings. Canadian Mathematical Bulletin, 14(1), 121-124. doi:10.4153/cmb-1971-024-9Hardy, G. E., & Rogers, T. D. (1973). A Generalization of a Fixed Point Theorem of Reich. Canadian Mathematical Bulletin, 16(2), 201-206. doi:10.4153/cmb-1973-036-0Karapinar, E., Agarwal, R., & Aydi, H. (2018). Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces. Mathematics, 6(11), 256. doi:10.3390/math6110256Karapınar, E., Alqahtani, O., & Aydi, H. (2018). On Interpolative Hardy-Rogers Type Contractions. Symmetry, 11(1), 8. doi:10.3390/sym11010008Aydi, H., Karapinar, E., & Roldán López de Hierro, A. (2019). ω-Interpolative Ćirić-Reich-Rus-Type Contractions. Mathematics, 7(1), 57. doi:10.3390/math7010057Debnath, P., & de La Sen, M. de L. (2019). Set-Valued Interpolative Hardy–Rogers and Set-Valued Reich–Rus–Ćirić-Type Contractions in b-Metric Spaces. Mathematics, 7(9), 849. doi:10.3390/math7090849Alqahtani, B., Fulga, A., & Karapınar, E. (2018). Fixed Point Results on Δ-Symmetric Quasi-Metric Space via Simulation Function with an Application to Ulam Stability. Mathematics, 6(10), 208. doi:10.3390/math6100208Aydi, H., Chen, C.-M., & Karapınar, E. (2019). Interpolative Ćirić-Reich-Rus Type Contractions via the Branciari Distance. Mathematics, 7(1), 84. doi:10.3390/math7010084Aydi, H., & Karapinar, E. (2012). A Meir-Keeler common type fixed point theorem on partial metric spaces. Fixed Point Theory and Applications, 2012(1). doi:10.1186/1687-1812-2012-26Ćirić, L., Samet, B., Aydi, H., & Vetro, C. (2011). Common fixed points of generalized contractions on partial metric spaces and an application. Applied Mathematics and Computation, 218(6), 2398-2406. doi:10.1016/j.amc.2011.07.005Karapınar, E., Chi, K. P., & Thanh, T. D. (2012). A Generalization of Ćirić Quasicontractions. Abstract and Applied Analysis, 2012, 1-9. doi:10.1155/2012/518734Mlaiki, N., Abodayeh, K., Aydi, H., Abdeljawad, T., & Abuloha, M. (2018). Rectangular Metric-Like Type Spaces and Related Fixed Points. Journal of Mathematics, 2018, 1-7. doi:10.1155/2018/3581768Gupta, A., & Gautam, P. (2016). Topological Structure of Quasi-Partial b-Metric Spaces. International Journal of Pure Mathematical Sciences, 17, 8-18. doi:10.18052/www.scipress.com/ijpms.17.8Gupta, A., & Gautam, P. (2015). Quasi-partial b-metric spaces and some related fixed point theorems. Fixed Point Theory and Applications, 2015(1). doi:10.1186/s13663-015-0260-

Dynamic Processes, Fixed Points, Endpoints, Asymmetric Structures, and Investigations Related to Caristi, Nadler, and Banach in Uniform Spaces

Research ArticleIn uniform spaces (...) with symmetric structures determined by the D-families of pseudometrics which define uniformity in these spaces, the new symmetric and asymmetric structures determined by the J-families of generalized pseudodistances on (...) are constructed; using these structures the set-valued contractions of two kinds of Nadler type are defined and the new and general theorems concerning the existence of fixed points and endpoints for such contractions are proved. Moreover, using these new structures, the single-valued contractions of two kinds of Banach type are defined and the new and general versions of the Banach uniqueness and iterate approximation of fixed point theorem for uniform spaces are established. Contractions defined and studied here are not necessarily continuous. One of the main key ideas in this paper is the application of our fixed point and endpoint version of Caristi type theorem for dissipative set-valued dynamic systems without lower semicontinuous entropies in uniform spaces with structures determined by J-families. Results are new also in locally convex and metric spaces. Examples are provided

Fixed Point Theorems for Set-Valued Mappings on TVS-Cone Metric Spaces

In the context of tvs-cone metric spaces, we prove a Bishop-Phelps and a Caristi's type theorem. These results allow us to prove a fixed point theorem for $(\delta, L)$-weak contraction according to a pseudo Hausdorff metric defined by means of a cone metric