Abstract metric spaces and Hardy-Rogers-type theorems

The purpose of the present paper is to establish coincidence point theorem for two mappings and fixed point theorem for one mapping in abstract metric space which satisfy contractive conditions of Hardy-Rogers type. Our results generalize fixed point theorems of Nemytzki [V.V. Nemytzki, Fixed point method in analysis, Uspekhi Mat. Nauk 1 (1936) 141-174], Edelstein I M. Edelstein, On fixed and periodic point under contractive mappings, J. Lond. Math. Soc. 37 (1962) 74-79] and Huang, Zhang [LG. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2)(2007) 1468-1476] from abstract metric spaces to symmetric spaces (Theorem 2.1) and to metric spaces (Theorem 2.4, Corollaries 2.6-2.8). Two examples are given to illustrate the usability of our results

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-

Implicit contractive maps in ordered metric spaces

Further extensions are given to the fixed point result (for implicit contractions) due to Altun and Simsek [Fixed Point Th. Appl., Volume 2010, Article ID 621469]. Some connections with related statements in the area due to Agarwal, El-Gebeily and O'Regan [Appl. Anal., 87 (2008), 109-116] are also discussed. Finally, the old approach in Turinici [An. St. Univ. "A. I. Cuza" Iasi, 22 (1976), 177-180] is presented, for historical reasons

Fixed Point Results for F-Contractive Mappings of Hardy-Rogers-Type

Recently,Wardowski introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, in this paper, we will present some fixed point results of Hardy-Rogers-type for self-mappings on complete metric spaces or complete ordered metric spaces. Moreover, an example is given to illustrate the usability of the obtained results

F-contractions of Hardy–Rogers type and application to multistage decision

We prove fixed point theorems for F-contractions of Hardy–Rogers type involving self-mappings defined on metric spaces and ordered metric spaces. An example and an application to multistage decision processes are given to show the usability of the obtained theorems