A discussion of Feng-Liu operator and fixed point theorems on metric space

[1] M. U. Ali, T. Kamram, W. Sintunavarat, P. Katchang, Mizoguchi-Takahashi’s fixed point theorem with α,η functions, Abstract and Applied Analysis 2013 (2013) 5–9.

[2] I. Altun, H. A. Hancer, U. Basar, Fixed point results for P-contractions via w-distance, Creative Mathematics and Informatics 32(1) (2023) 13–20.

[3] I. Altun, H. A. Hancer, A. Erduran, Fixed point results for single valued and set valued Pcontractions and application to second order boundary value problems, Carpathian Journal of Mathematics 36(2) (2020) 205–214.

[4] I. Altun, H. Dag, Nonlinear proximinal multivalued contractions on quasi-metric spaces, Journal of Fixed Point Theory and Applications (2017) DOI 10.1007/s1 1784-017-0436-y.

[5] I. Altun, A. H. Hancer, U. Basar, Fixed point results for P-contractions via w-distance, Creative Mathematics and Informatics 32(1) (2023) 13–20.

[6] I. Altun, M.Olgun, G.Minak,Onanewclassofmulti-valuedweaklyPicardoperatorsoncomplete metric spaces, Taiwanese Journal of Mathematics 19(3) (2015) 659–672.

[7] I. Altun, G. Minak, M. Olgun, Fixed points of multi-valued nonlinear F-contractions on complete metric spaces, Nonlinear Analysis: Modelling and Control 21(2) (2016) 201–210.

[8] A. Amini-Harandi, M. Fakhar, H. R. Hajisharifi, Fixed point theorems for set-valued contractions, Rendiconti del Circolo Matematico di Palermo (2013) DOI 10.1007/s12215-013-0130-x.

[9] H. J. Asl, S. Rezapour, N. Shahzad, On fixed points of α-psi-contractive multi-functions, Journal of Fixed Point Theory and Applications 2012(6) (2012) 212–218.

[10] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fundamental Mathematicae 3(1) (1922) 133–181.

[11] V. Berinde, M. Päcurar, Iterative Approximation of Fixed Points of Single-valued Almost Contractions, in Fixed Point Theory and Graph Theory, Elsevier/Academic Press, Amsterdam (2016) 29–97.

[12] B. A. Bin Dehaish, A. Latif, Fixed point theorems for generalized contractive type multivalued maps, Journal of Fixed Point Theory and Applications 2012 (2012) 135.

[13] B. S. Choudhury, N. Metiya, S. Kundu, A multivalued fixed point result with associated data dependece and stability study, Problemy Analiza. Issues of Analysis 11(1) (2022) 45–57.

[14] L. Ciric, Fixed point theorems for multi-valued contractions in complete metric spaces, Journal of Mathematical Analysis and Applications 348(1) (2008) 499–507.

[15] L. Ciric, Multi-valued nonlinear contraction mappings, Nonlinear Analysis: Theory, Methods and Applications 71(7) (2009) 2716–2723.

[16] G.Durmaz,I.Altun, OnNonlinearSet-Valued θ-Contractions. Bulletin of the Malaysian Mathematical Sciences Society (2018) https://doi.org/10.1007/s40840-018-0689-7.

[17] J. G. Falset, L. Guran, E. Llorens-Fuster, Fixed points for mulit-valued contractions with respect to a w-distance, Scientiae Mathematicae Japonicae Online e-2009 (2009) 611–619.

[18] Y. Feng, S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi’s fixed point theorems, Journal of Mathematical Analysis and Applicatios 317 (2006) 103112.

[19] L. Guran, Fixed points for multi–valued operators with respect to a w-distance on metric spaces, Carpathian Journal of Mathematics 23(2) (2007) 89–92.

[20] T. L. Hicks, B. E. Rhoades, A banach type fixed point theorem, Japanese Journal of Mathematics 24 (1979) 327–330. [21] H. A. Hancer, M. Olgun, I. Altun, Some new types multivalued F-contractions on quasi metric spaces and their fixed points, Carpathian Journal of Mathematics 35(1) (2019) 41–50.

[22] L.G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings. Journal of Mathematical Analysis and Applications 332 (2007) 1468–1476.

[23] N. Hussain, G. Ali, I. Iqbal, B. Samet, The Existence of Solutions to Nonlinear Matrix Equations via Fixed Points of Multivalued F-Contractions, Mathematics 8(2) (2020) 212.

[24] A. Hussain, M. Arshad, S. U. Khan, τ-Generalization of fixed point results for F-contractions, International Journal of Mathematics and Computer Science 1 (2015) 127–137.

[25] N. Hussain, M. A. Kutbi, P. Salimi, Fixed point theory in α-complete metric spaces with applications, In Abstract and Applied Analysis 2014 (2014) 1–11.

[26] N. Hussain, P. Salimi, A. Latif, Fixed point results for single and set-valued α − η − ψ-contractive mappings, Journal of Fixed Point Theory and Applications 2013 (2013) 212–235.

[27] N. Hussain, N. Yasmin, N. Shafqat, Multi-Valued Ciric Contractions on Metric Spaces with Applications, University of Nis, Faculty of Sciences and Mathematics 28(9) (2014) 1953–1964.

[28] I. Iqbal, N. Hussain, Fixed point theorems for generalized multi-valued nonlinear F-contractions, Journal of Nonlinear Science and Application 9 (2016) 5870–5893.

[29] O. Kada, T. Suzuki, W. Takahashi, Nonconvex minimization theorems and fixed points theorems in complete metric space, Scientiae Mathematicae Japonicae, 44 (1996) 381–391.

[30] T. Kamran, Mizoguchi-Takahashi’s type fixed point theorem Computers and Mathematics with Applications 57(3) (2009) 507–511.

[31] T. Kamran, Fixed point theorems for hybrid mappings satisfying an integral type contractive condition, Georgian Mathematical Journal 19 (2012) 117–125.

[32] H. Kaneko, Single-valued and multivalued f-contractions, Bollettino dell Unione Matematica Italiana, A(6) 4(1) (1985) 29–33.

[33] D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, Journal of Mathematical Analysis and Applications 334(1) (2007) 132–139.

[34] A. Latif, A. A. N. Abdou, Fixed points of generalized contractive maps, Journal of Fixed Point Theory and Applications 2009 (2009) https://doi.org/10.1155/2009/487161

[35] A. Latif, A. A. N.Abdou, Some new weakly contractive type multimaps and fixed point results in metric spaces, Journal of Fixed Point Theory and Applications 2009 (2009) 12.

[36] A. Latif, A. A. N. Abdou, Multi-valued generalized nonlinear contractive maps and fixed points, Nonlinear Analysis 74 (2011) 1436–1444.

[37] A. Latif, A. A. N. Abdou, Fixed point results for generalized contractive multimaps in metric spaces, Journal of Fixed Point Theory and Applications (2009) 16.

[38] A. Latif, W. A. Albar, Fixed point results in complete metric spaces, Demonstratio Mathematica 41(1) (2008) 145–150. [39] L. Lin, C. Chuang, Some new fixed point theorems of generalized nonlinear contractive multivalued maps in complete metric spaces, Computers and Mathematics with Applications 62 (2011) 3555–3566.

[40] L. J. Lin, W. S. Du, Ekeland’s variational principle, minimax theorems and existence of nonconvex equilibria in complete metric spaces, Journal of Mathematical Analysis Applications 323 (2006) 360–370.

[41] Z. Liu, Y. Lu, S. M. Kang, Fixed point theorems for multi-valued contractions with w-distance, Applied Mathematics and Computation 224 (2013) 535–552.

[42] Z. Liu, W. Sun, S. M. Kang, J. S. Ume, On fixed point theorems for multi-valued contractions, Journal of Fixed Point Theory and Applications 2010 (2010) 18.

[43] G.Minak, M.Olgun,I.Altun, Anewapproachtofixedpointtheoremsformultivaluedcontractive maps, Carpathian Journal of Mathematics 31(2) (2015) 241-248.

[44] N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, Journal of Mathemacal Analysis and Applications 141 (1989) 177–188.

[45] S. B. Nadler, Multi-valued contraction mappings, Pacific Journal of Mathematics30(1969)475–488.

[46] H. K. Nashine, L. K. Dey, R. W. Ibrahim, S. Radenovic, Feng-Liu-type fixed point result in orbital b-metric spaces and application to fractal integral equation, Nonlinear Analysis: Modelling and Control 26(3) (2021) 522–533.

[47] H. K. Nashine, Z. Kadelburg, Wardowski-Feng-Liu Type Fixed Point Theorems FOR Multi-valued Mappings, Fixed Point Theory 21(2) (2020) 697–706.

[48] A. Nicolae, Fixed point theorems for multi-valued mappings of Feng-Liu type, Fixed Point Theory 12 (2011) 145–154. [49] H.K.Pathak, I. Beg, Fixed point of multivalued contractions by altering distances with application to nonconvex Hammerstein type integral inclusions, Fixed Point Theory 22(1) (2021) 327–342.

[50] H. K. Pathak, N. Shahzad, Fixed point results for set-valued contractions by altering distances in complete metric spaces, Nonlinear Analysis: Theory, Methods and Applications 70(7) (2009) 26342641.

[51] T. Rasham, M. S. Shabbir, M. Nazam, A. Musatafa, C. Park, Orbital b-metric spaces and related f ixed point results on advanced Nashine-Wardowski-Feng-Liu type contractions with applications, Journal of Inequalities and Applications 2023 (1) (2023) 69.

[52] S. Reich, Fixed points of contractive functions, Bolletino dell’Unione Mathematica Italiana 5 (1972) 26–42.

[53] B. E. Rhoades, A comparison of various definitions of contractive mappings, Transactions of the American Mathematical Society 226 (1977) 257–290.

[54] H. Sahin, M. Aslantas, I. Altun, Feng-Liu type approach to best proximity point results for multivalued mappings, Journal of Fixed Point Theory and Applications 22 (2019) 11–23.

[55] H. Sahin, M. Aslantas, A. A. Nasir Nasir, Some extended results for multivalued F-contraction mappings, Axioms 12(2)(2023) 116.

[56] H. Sahin, I. Altun, D. Turkoglu, Fixed point results for mixed multi-valued mappings of Feng-Liu type on Mb-metric spaces, Nonlinear System and Complexity 23 (2019) 67–80.

[57] B. Samet, C. Vetro, F. Vetro, Fixed point theorems for α-psi-contractive type mappings. Nonlinear Analysis 75 (2012) 2154–2165.

[58] B. Samet, C. Vetro, F. Vetro, An approximate fixed point result for multivalued mappings under twoconstraint inequalities, Journal of Fixed Point Theory and Applications (2012) DOI 10.1007/s1 1784-016-0399-4.

[59] M.S.Shagari, T. Alotaibi, R. Tabassum, A. A. Bakery, O. K. S. Mohamed, A. O.Mustafa, Feng-Liu’s Approach to Fixed Point Results of Intuitionistic Fuzzy Set-Valued Maps, Symmetry 15(4) (2023) 930.

[60] M. S. Shagari, S. Rashid, K. M. Abualnaja, M. Alansari, On nonlinear fuzzy set-valued Θcontractions with applications, AIMS Mathematics 6(10) (2021) 10431–10448.

[61] W. Takahashi, Existence theorems generalizing fixed point theorems for multivalued mappings, in Journal of Fixed Point Theory and Applications, (M.A: Thera and J.B. Baillon Eds.), Pitman Research Notes in Mathematics Series 252 (1991) 397–406.

[62] J. S. Ume, Existence theorems for generalized distance on complete metric space, Journal of Fixed Point Theory and Applications, Article ID 397150(2010).

[63] J. S. Ume ,B. S. Lee, S. J. Cho, Some results on fixed point theorems for multivalued mappings in complete matric spaces, International Journal of Mathematics and Mathematical Sciences (2002) 319–325.

[64] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Journal of Fixed Point Theory and Applications 94 (2012) 6.