Multivalued Nonlinear Weakly Picard Operators in Metric Spaces
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Abstract
In this paper, the concept of -contraction was presented and a new fixed-point theorem for such contractions would be established. We provide applications to prove that there is a fixed point for cyclic mappings. We also received fixed-point results for the weak contraction type mappings.
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References
Nadler SB, Multivalued contraction mappings. Pac. J. Math. 1969; 30, 475-488.
Berinde V, Approximating fixed points of weak contractions using the Picard iteration. Nonlinear Anal Forum. 2004; 9, 43-53.
Berinde V, General constructive fixed point theorems for Ciric-type almost contractions in metric spaces. Carpath. J. Math. 2008; 24, 10-19.
Berinde M, Berinde V, On a general class of multivalued weakly Picard mappings. J. Math. Anal. 2007; 326, 772-782.
Popescu O, A new type of contractive multivalued operators. Bull. Sci. Mat. 2013; 137, 30-44.
Kamran T, Hussain S, Weakly (s,r)-contractive multi-valued operators. Rend. Circ. Mat. Palermo. 2015; 64, 475-482.
Wardowski D, Fixed point of a new type of contractive type of mappings in complete metric spaces. Fixed Point Theory Appl. 2012; 2012, 94.
Turinici M, Wardowski implicit contractions in metric spaces, (2013). arXiv:1212.3164v2.
Petrusel A, Rus AI, Santamaaria. Biol. Chem. 2003; 290, 21352-21364.
Altun I, Durmaz G, Minak G, Romaguera S, Multivalued almost F-contractions on complete metric spaces. Filomat. 2016; 30(2), 441-448.
Kitkuan D, Suzuki-type Z-contraction performance. J. Math. Comput. Sci. 2021; 11(6), 6857-6871.
Padcharoen A, Kumam P, Saipara P, Chaipunya P, Generalized Suzuki type Z-contraction in complete metric spaces. Kragujevac Journal of Mathematics. 2018; 42(3), 419-430.
Saipara P, Kumam P, Bunpatcharacharoen P, Some Results for Generalized Suzuki Type Z-Contraction in Metric Spaces. Thai Journal of Mathematics, 2018; SI, 203-219.
Bunpatcharacharoen P, Saelee S, Saipara P, Modified almost type Z-contraction. Thai Journal of Mathematics. 2020; 18(1), 252-260.
Padcharoen A, Kim JK, Berinde type results via simulation functions in metric spaces. Nonlinear Functional Analysis and Applications. 2020; 25(3), 511-523.
Latif A, Abdou AAN, Multivalued generalized nonlinear contractive maps and fixed points. Nonlinear Anal. 2011; 74, 1436-1444.