Set-valued fixed point results with application to Fredholm-type integral inclusion

References

• Neumann JV. Zur theorie der gesellschaftsspiele. (German) Math Ann. 1928;100(1):295–320. doi: 10.1007/BF01448847
   Google Scholar
• Kakutani S. A generalization of Brouwer's fixed point theorem. Duke Math J. 1941;7:457–459. doi: 10.1215/S0012-7094-41-00838-4
   Google Scholar
• Bohnenblust HF, Karlin S. On a theorem of Ville. Contributions to the theory of games. Princeton (NJ): Princeton University Press; 1950. p. 155–160. (Annals of Mathematics Studies; 24).
   Google Scholar
• Nadler Jr SB. Multi-valued contraction mappings. Pacific J Math. 1969;30:475–488. doi: 10.2140/pjm.1969.30.475
   Web of Science ®Google Scholar
• Branciari A. A fixed point theorem for mapping satisfying a general contractive condition of integral type. Int J Math Math Sci. 2002;29:531–536. doi: 10.1155/S0161171202007524
   Google Scholar
• Liu Z, Li X, Kang SM, et al. Fixed point theorems for mappings satisfying contractive conditions of integral type and applications. Fixed Point Theory Appl. 2011;2011:64. 18 pp. doi: 10.1186/1687-1812-2011-64
   Google Scholar
• Akram M, Zafar AA, Siddiqui AA. A general class of contractions: A- contractions. Novi Sad J Math. 2008;38:25–33.
   Google Scholar
• Kannan R. Some results on fixed points. Bull Calcutta Math Soc. 1968;60:71–76.
   Google Scholar
• Bianchini R. Su un problema di S. Reich riguardante la teori dei punti fissi. Boll Un Math Ital. 1972;5:103–108.
   Google Scholar
• Reich S. Kannan's fixed point theorem. Boll Un Math Ital. 1971;4:1–11.
   Google Scholar
• Sahaa M, Deyb D. Fixed point theorems for A-contraction mappings of integral type. J Nonlinear Sci Appl. 2012;5:84–92. doi: 10.22436/jnsa.005.02.02
   Google Scholar
• Samet B, Vetro C, Vetro P. Fixed point theorem for α−ψ− contractive type mappings. Nonlinear Anal. 2012;75:2154–2165. doi: 10.1016/j.na.2011.10.014
   Web of Science ®Google Scholar
• Hussain K, Salimi A. α-admissible mappings and related fixed point theorems. J Inequal Appl. 2013;2013:114. doi: 10.1186/1029-242X-2013-114
   Google Scholar
• Salimi P, Latif A, Hussain N. Modified α−ψ- contractive mappings with applications. Fixed Point Theory Appl. 2013;2013:151. doi: 10.1186/1687-1812-2013-151
   Google Scholar
• Karapınar E, Samet B. Generalized α−ψ contractive type mappings and related fixed point theorems with applications. Abstr Appl Anal. 2012; 2012: ID 793486, 17 pp.
   Google Scholar
• Asl JH, Rezapour S, Shahzad N. On fixed point of α−ψ-contractive multifunctions. Fixed Point Theory Appl. 2012;2012:212. doi: 10.1186/1687-1812-2012-212
   Google Scholar
• Hussain N, Salimi P, Latif A. Fixed point results for single and set-valued α−η−ψ-contractive mappings. Fixed Point Theory Appl. 2013;2013:2012.
   Google Scholar
• Radenovic S, Kadelburg Z, Jandrlic D, et al. Some results on weakly contractive maps. Bul Iran Math Soc. 2012;38:325–645.
   Web of Science ®Google Scholar
• Chandok S, Ansari AH, Došenović T, et al. On αβ-contractive and admissible mappings. Miskolc Math Notes. 2018;19(2):787–793. doi: 10.18514/MMN.2018.2077
   Google Scholar
• Geraghty M. On contractive mappings. Proc Amer Math Soc. 1973;40:604–608. doi: 10.1090/S0002-9939-1973-0334176-5
   Web of Science ®Google Scholar
• Banach S. Sur les opeerations dans les ensembles abstraits et leur application aux equations integrales. Fund Math. 1992;3:133–181. doi: 10.4064/fm-3-1-133-181
   Google Scholar
• Dube LS. A theorem on common fixed points of multi-valued mappings. Ann Soc Sci Bruxelles Sér I. 1975;89(4):463–468.
   Google Scholar
• Babu GVR, Sailaja PD. A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces. Thai J Math. 2011;9:1–10.
   Google Scholar
• Deep A, Deepmala X, Tunç C. On the existence of solutions of some non-linear functional integral equations in Banach algebra with applications. Arab J Basic Appl Sci. 2020;27(1):279–286. doi: 10.1080/25765299.2020.1796199
   Google Scholar
• Tunç C. A remark on the qualitative conditions of nonlinear IDEs. Int J Math Comput Sci. 2020;3:905–922.
   Google Scholar
• Tunç C, Tunç O. New qualitative criteria for solutions of Volterra integro-differential equations. Arab J Basic Appl Sci. 2018;25(3):158–165. doi: 10.1080/25765299.2018.1509554
   Google Scholar
• Tunç C, Tunç O. New results on the stability, integrability and boundedness in Volterra integro-differential equations. Bull Comput Appl Math. 2018;6(1):41–58.
   Web of Science ®Google Scholar
• Tunç C, Tunç O. On behaviors of functional Volterra integro-differential equations with multiple time-lags. J Taibah Univ Sci. 2018;12(2):173–179. doi: 10.1080/16583655.2018.1451117
   Web of Science ®Google Scholar
• Tunç C, Tunç O. A note on the qualitative analysis of Volterra integro-differential equations. J Taibah Univ Sci. 2019;13(1):490–496. doi: 10.1080/16583655.2019.1596629
   Web of Science ®Google Scholar
• Shang Y. Scaled consensus of switched multi-agent systems. IMA J Math Control and Information. 2019;36:639–657. doi: 10.1093/imamci/dnx062
   Web of Science ®Google Scholar
• Shang Y. Continuous-time average consensus under dynamically changing topologies and multiple time-varying delays. Appl Math Comput. 2014;244:457–466.
   Web of Science ®Google Scholar
• Al-Sulami H, Ahmad J, Hussain N, et al. Solutions to Fredholm integral inclusions via generalized fuzzy contractions. Mathematics. 2019;7:1–9.
   Web of Science ®Google Scholar
• Abdullah AS, Ahmad J. Generalized fixed-point results for almost (α,Fσ)-contractions with applications to Fredholm integral inclusions. Symmetry. 2019;11:1–9.
   Google Scholar
• Sîntămărian A. Integral inclusions of Fredholm type relative to multivalued φ-contractions. International Conference on Nonlinear Operators, Differential Equations and Applications (Cluj-Napoca, 2001). Semin. Fixed Point Theory Cluj-Napoca 3 2002. p. 361–36
   Google Scholar
• Ali MU, Kamran T, Postolache M. Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem. Nonlinear Anal Model Control. 2017;22(1):17–30. doi: 10.15388/NA.2017.1.2
   Web of Science ®Google Scholar
• Shang Y, Ye Y. Fixed-time group tracking control with unknown inherent nonlinear dynamics. IEEE Access. 2017;14:1–9. doi: 10.1109/ACCESS.2017.2737633
   Google Scholar
• Salem A, Al-Dosari A. Existence results of solution for fractional Sturm-Liouville inclusion involving composition with multi-maps. J Taibah University for Sci. 2020;14:721–733. doi: 10.1080/16583655.2020.1771834
   Web of Science ®Google Scholar
• Meknani B. The existence and uniqueness of integral solutions to some nonlinear reaction-diffusion system with nonlocal retarded initial conditions. J Taibah University for Sci. 2020;14:569–578. doi: 10.1080/16583655.2020.1751441
   Web of Science ®Google Scholar