Measures of noncompactness in modular spaces and fixed point theorems for multivalued nonexpansive mappings

Abdou, A.A.N., Khamsi, M.A.: Fixed point theorems in modular vector spaces. J. Nonlinear Sci. Appl. 10(8), 4046–4057 (2017) Ayerbe, J.M., Domínguez Benavides, T., López Acedo, G.: Measures of Noncompactness in Metric Fixed Point Theory. Birkhäuser (1997) Bachar, M., Bounkhel, M., Khamsi, M.A.: Uniform Convexity in lp(.). J. Nonlinear Sci. Appl. 10, 5292–5299 (2017) Bachar, M., Mendez, O., Bounkhel, M.: Modular uniform convexity of Lebesgue spaces of variable integrability. Symmetry 10(12), 708 (2018). https://doi.org/10.3390/sym10120708 Browder, F.E.: Fixed point theorems for noncompact mappings in Hilbert spaces. Proc. Nat. Acad. Sci. USA 43, 1272–1276 (1965) Browder, F.E.: Nonexpansive nonlinear opemtors in a Banach space. Proc. Nat. Acad. Sci. USA 54, 1041–1044 (1965) Dhompongsa, S., Domínguez Benavides, T., Kaewcharoen, A., Panyanak, B.: Fixed point theorems for multivalued mappings in modular function spaces. Sci. Math. Jpn. 63(2), 161–169 (2006) Domínguez Benavides, T.: Geometric properties of Banach spaces and metric fixed point theory. Extracta Math. 17, 331–349 (2002) Domínguez Benavides, T., Gavira, B.: Does Kirk’s theorem holds for multivalued nonexpansive mappings? Fixed Point Theory Appl. 2010, 546761 (2010). https://doi.org/10.1155/2010/546761 Domínguez Benavides, T., Japón, M.: Fixed point properties and reflexivity in variable Lebesgue spaces. J. Funct. Anal. 280(6), 108896 (2021). https://doi.org/10.1016/j.jfa.2020.108896 Domínguez Benavides, T., Khamsi, M.A., Samadi, S.: Asymptotically regular mappings in modular function spaces. Sci. Math. Jpn. 53(2), 295–304 (2001) Domínguez Benavides, T., Lorenzo, P.: Fixed point theorems for multivalued nonexpansive mappings without uniform convexity. Abs. Appl. Anal. 6(2003), 375–386 (2003) Domínguez Benavides, T., Lorenzo, P.: Asymptotic centers and fixed points for multivalued nonexpansive mappings. Ann. Univ. Mariae Curie-Sklodowska Sect. A 58, 37–45 (2004) Domínguez Benavides, T., Moshtaghioun, S.M., Sadeghi Hafshejani, A.: Fixed points for several classes of mappings in Variable Lebesgue Spaces. Optimization. https://doi.org/10.1080/02331934.2019.1711086 Goebel, K.: On a fixed point theorem for multivalued nonexpansive mappings. Ann. Univ. Marie Curie-Sklodowska 29, 70–72 (1975) Goebel, K., Kirk, W.A.: Topics in Metric Fixed Point Theory. Cambridge University Press (1990) Goebel, K., Sekowski, T.: The modulus of noncompact convexity. Ann. Univ. Mariae Curie-Sklodowska Sect. A 38, 41–48 (1984) Göhde, D.: Zum Prinzip der kontraktiven Abbildung. Math. Nach. 30, 251–258 (1965) Hu, S., Papageorgiou, N.: Handbook of Multivalued Analysis, vol. 1. Kluwer Academic Publishers, Dordrecht (1997) Kamińska, A.: On unifrom convexity of Orlicz spaces. Nederl. Akad. Wetensch. Indag. Math. 44(1), 27–36 (1982) Khamsi, M.A., Kozlowski, W.M.: Fixed Point Theory in Modular Function Spaces. Birkäuser, Basel (2015) Khamsi, M.A., Kozlowski, W.M., Reich, S.: Fixed point theory in modular function spaces. Nonlinear Anal. 14(11), 935–953 (1990) Kozlowski, W.M.: Modular function spaces. Dekker, New York (1988) Kirk, W.A.: A fixed point theorem for mappings which do not increase the distances. Am. Math. Mon. 72, 1004–1006 (1965) Kirk, W.A., Massa, S.: Remarks on asymptotic and Chebyshev centers. Houston J. Math. 16(3), 357–364 (1990) Kuczumov, T., Prus, S.: Asymptotic centers and fixed points of multivalued nonexpansive mappings. Houst. J. Math. 16, 465–468 (1990) Lim, T.C.: A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space. Bull. Am. Math. Soc. 80, 1123–1126 (1974) Musielak, J., Orlicz, W.: On modular spaces. Studia Math. 18, 591–597 (1959) Nakano, H.: Modulared Semi-ordered Linear Spaces. Maruzen Co., Tokyo (1950) Nakano, H.: Topology of Linear Topological Spaces. Maruzen Co. Ltd, Tokyo (1951) Orlicz, W.: Über konjugierte Exponentenfolgen. Studia Math. 3, 200–212 (1931) Reich, S.: Some fixed point problems. Atti Accad. Naz. Lincei 57, 194–198 (1974) Reich, S.: Approximate selections, best approximations, fixed points, and invariant sets. J. Math. Anal. Appl. 62, 104–113 (1978) Ru̇žička, M.: Electrorheological Fluids: Modeling and Mathematical Theory. Lecture Notes in Mathematics, vol. 1748. Springer, Berlin (2000)