Novel Generalisation of Some Fixed Point Results Using a New Type of Simulation Function
Subject Areas : Transactions on Fuzzy Sets and Systems
1 - Department of Applied Sciences, ISB&M, College of Engineering, Associate professor, Pune, India.
Keywords: Metric space, Fuzzy metric space, Fuzzy metric-like space, α-Admissible MA-simulation function.,
Abstract :
I am utilizing a brand-new simulation function that has previously been developed by eminent mathematicians and that uses fuzzy metric-like spaces to establish new fixed point theorems. Here, this is demonstrated that the current conclusion is unquestionably a unified one that can generalize earlier current results. To further demonstrate the relevance of my findings, a few additional theorems and corollaries are demonstrated. Additionally, several excellent examples are provided to show how useful my findings are. I provide an application of my major finding in the conclusion.
[1] Menger M. Probabilistic geometry. Proceedings of the National Academy of Sciences. 1951; 37(4): 226- 229. DOI: https://doi.org/10.1073/pnas.37.4.226
[2] Kramosil I, Michalek J. Fuzzy metrics and statistical metric spaces. Kybernetika. 1975; 11(5): 336-344. https://www.kybernetika.cz/content/1975/5/336/paper.pdf
[3] George A, Veeramani P. On some results in fuzzy metric spaces. Fuzzy sets and systems. 1994; 64(3): 395-399. DOI: https://doi.org/10.1016/0165-0114(94)90162-7
[4] George A, Veeramani P. On some results of analysis for fuzzy metric spaces. Fuzzy sets and systems. 1997; 90(3): 365-368. DOI: https://doi.org/10.1016/S0165-0114(96)00207-2
[5] Argoubi H, Samet B, Vetro C. Nonlinear contractions involving simulation functions in a metric space with a partial order. Journal of Nonlinear Science and Applications. 2015; 8(6): 1082-1094. DOI: http://dx.doi.org/10.22436/jnsa.008.06.18
[6] Roldan-Lopez-de-Hierro AF, Kerapinar E, Roldan-Lopez-de-Hierro C, Martinez-Moreno J. Coincidence point theorems on metric spaces via simulation functions. Journal of Computational and Applied Mathematics. 2015; 275: 345-355. DOI: http://dx.doi.org/10.1016/j.cam.2014.07.011
[7] Karapinar E. Fixed points results via simulation functions. Filomat. 2016; 30(8): 2343-2350. DOI: https://doi:10.2298/FIL1608343K
[8] Khojasteh F, Shukla S, Radenovic S. A new approalh to the study of fixed point theory for simucation functions. Filomat. 2015; 29(6): 1189-1194. DOI: http://dx.doi.org/10.2298/FIL1506189K
[9] Perveen A, Imdad M. Proving new fixed point results in fuzzy metric spaces employing simulation function. Journal of Intelligent & Fuzzy Systems. 2019; 36(6): 6493-6501. DOI: http://dx.doi.org/10.3233/JIFS-182873
[10] Moussaoui A, Hussain N, Mellian S, Nasr H, Imdad M. Fixed point results via extended FZ-simulation functions in fuzzy metric spaces. Journal of Inequalities and Applications. 2022; 2022(1): 69. DOI: https://doi.org/10.1186/s13660-022-02806-z
[11] Schweizer B, Sklar A. Statistical metric spaces. Pacific J. Math. 1960; 10(1): 313-334. https://msp.org/pjm/1960/10-1/pjm-v10-n1-p20-p.pdf
[12] Gregori V, Sapena A. On fixed-point theorems in fuzzy metric spaces. Fuzzy sets and Systems. 2002; 125(2) : 245-252. DOI: https://doi.org/10.1016/S0165-0114(00)00088-9
[13] Roldan-Lopez-de-Hierro AF, Kerapinar E, Manro S. Some new fixed point theorems in fuzzy metric spaces. Journal of Intelligent & Fuzzy Systems. 2014; 27(5): 2257-2264. DOI: http://dx.doi.org/10.3233/IFS-141189
[14] Sapena A. A contribution to the study of fuzzy metric spaces. Applied General Topology. 2001; 2(1): 63-75. DOI: http://dx.doi.org/10.4995/agt.2001.3016
[15] Grabiec M. Fixed points in fuzzy metric spaces. Fuzzy sets and systems. 1988; 27(3): 385-389. DOI: https://doi.org/10.1016/0165-0114(88)90064-4
[16] Shukla S, Abbas M. Fixed point results in fuzzy metric-like spaces. Iranian Journal of Fuzzy Systems. 2014; 11(5): 81-92. DOI: https://doi.org/10.22111/ijfs.2014.1724
[17] Amini-Harandi A. Metric-like spaces, partial metric spaces and fixed points. Fixed point theory and applications. 2012; 1-10. DOI: http://dx.doi.org/10.1186/1687-1812-2012-204
[18] Gopal D, Vetro C. Some new fixed point theorems in fuzzy metric spames. Iranian Journal of Fuzzy Systems. 2014; 11(3): 95-107. DOI: https://doi.org/10.22111/ijfs.2014.1572
[19] Dinarvand M. Some fixed point results for admissible Geraghty contraction type mappings in fuzey mztric spaces. Iranian journal of fuzzy systems. 2017; 14(3): 161-177. DOI: https://doi.org/10.22111/ijfs.2017.3262
[20] Banach S. Sur les operations dans les ensembles abstraits et leur application aux equations integrales. Fundamenta mathematicae. 1922; 3(1): 133-181. https://eudml.org/doc/213289
[21] Boyd DW, Wong JSW. On nonlinear contractions. Proceedings of the American Mathematical Society. 1969; 20(2): 458-464. https://www.ams.org/journals/proc/1969-020-02/S0002-9939-1969-0239559-9/
[22] Abbas M, Imdad M, Gopal D. ψ- weak contractions in fuzzy metric spaces. Iranian Journal of Fuzzy Systems. 2011; 8(5): 141-148. DOI: https://doi.org/10.22111/ijfs.2011.303