×

zbMATH — the first resource for mathematics

Solvability of integrodifferential problems via fixed point theory in \(b\)-metric spaces. (English) Zbl 06585788
Summary: The purpose of this paper is to study the existence of solutions set of integrodifferential problems in Banach spaces. We obtain our results by using fixed point theorems for multivalued mappings, under new contractive conditions, in the setting of complete \(b\)-metric spaces. Also, we present a data dependence theorem for the solutions set of fixed point problems.

MSC:
47H10 Fixed-point theorems
34A60 Ordinary differential inclusions
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Cabada, A; Infante, G; Tojo, FAF, Nontrivial solutions of Hammerstein integral equations with reflections, Bound. Value Probl., 2013, (2013) · Zbl 1294.45002
[2] Agarwal, RP; O’Regan, D; Wong, PJY, Existence results of Brezis-Browder type for systems of Fredholm integral inclusions, Adv. Differ. Equ., 2011, (2011) · Zbl 1271.45002
[3] Petruşel, A, Integral inclusions. fixed point approaches, Comment. Math. Prace Mat., 40, 147-158, (2000) · Zbl 0991.47041
[4] Sîntămărian, A, Integral inclusions of Fredholm type relative to multivalued \(φ\)-contractions, No. 3, 361-368, (2002) · Zbl 1028.47043
[5] Nadler, SB, Multivalued contraction mappings, Pac. J. Math., 30, 475-488, (1969) · Zbl 0187.45002
[6] Abbas, M; Ali, B; Vetro, C, A Suzuki type fixed point theorem for a generalized multivalued mapping on partial Hausdorff metric spaces, Topol. Appl., 160, 553-563, (2013) · Zbl 1264.54054
[7] Amini-Harandi, A, Fixed point theory for set-valued quasi-contraction maps in metric spaces, Appl. Math. Lett., 24, 1791-1794, (2011) · Zbl 1230.54034
[8] Altun, I; Minak, G; Dağ, H, Multi-valued \(F\)-contractions on complete metric spaces, J. Nonlinear Convex Anal., 16, 659-666, (2015) · Zbl 1315.54032
[9] Aydi, H; Abbas, M; Vetro, C, Partial Hausdorff metric and nadler’s fixed point theorem on partial metric spaces, Topol. Appl., 159, 3234-3242, (2012) · Zbl 1252.54027
[10] Chifu, C; Petruşel, G, Existence and data dependence of fixed points and strict fixed points for contractive-type multivalued operators, Fixed Point Theory Appl., 2007, (2007) · Zbl 1155.54337
[11] Daffer, PZ; Kaneko, H, Fixed points of generalized contractive multi-valued mappings, J. Math. Anal. Appl., 192, 655-666, (1995) · Zbl 0835.54028
[12] Reich, S, Approximate selections, best approximations, fixed points, and invariant sets, J. Math. Anal. Appl., 62, 104-113, (1978) · Zbl 0375.47031
[13] Reich, S, Fixed points of contractive function, Boll. Unione Mat. Ital., 5, 26-42, (1972) · Zbl 0249.54026
[14] Wardowski, D, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012, (2012) · Zbl 1310.54074
[15] Sgroi, M; Vetro, C, Multi-valued \(F\)-contractions and the solution of certain functional and integral equations, Filomat, 27, 1259-1268, (2013) · Zbl 1340.54080
[16] Feng, Y; Liu, S, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl., 317, 103-112, (2006) · Zbl 1094.47049
[17] Czerwik, S, Nonlinear set-valued contraction mappings in \(b\)-metric spaces, Atti Semin. Mat. Fis. Univ. Modena, 46, 263-276, (1998) · Zbl 0920.47050
[18] Bakhtin, IA, The contraction mapping principle in quasimetric spaces, No. 30, 26-37, (1989), Ul’yanovsk
[19] Berinde, V, Generalized contractions in quasimetric spaces, 3-9, (1993) · Zbl 0878.54035
[20] Boriceanu, M; Bota, M; Petruşel, A, Multivalued fractals in \(b\)-metric spaces, Cent. Eur. J. Math., 8, 367-377, (2010) · Zbl 1235.54011
[21] Boriceanu, M; Petruşel, A; Rus, IA, Fixed point theorems for some multivalued generalized contractions in \(b\)-metric spaces, Int. J. Math. Stat., 6, 65-76, (2010)
[22] Bota, M; Molinár, A; Varga, C, On ekeland’s variational principle in \(b\)-metric spaces, Fixed Point Theory, 12, 21-28, (2011) · Zbl 1278.54022
[23] Cosentino, M; Salimi, P; Vetro, P, Fixed point results on metric-type spaces, Acta Math. Sci., 34, 1237-1253, (2014) · Zbl 1324.54065
[24] Czerwik, S; Dlutek, K; Singh, SL, Round-off stability of iteration procedures for set-valued operators in \(b\)-metric spaces, J. Natur. Phys. Sci., 11, 87-94, (2007) · Zbl 0968.54031
[25] Paesano, D; Vetro, P, Fixed point theorems for \(α\)-set-valued quasi-contractions in \(b\)-metric spaces, J. Nonlinear Convex Anal., 16, 685-696, (2015) · Zbl 1315.54041
[26] Aydi, H; Bota, M-F; Karapinar, E; Mitrović, S, A fixed point theorem for set-valued quasicontractions in b-metric spaces, Fixed Point Theory Appl., 2012, (2012) · Zbl 06215370
[27] Czerwik, S, Contraction mappings in \(b\)-metric spaces, Acta Math. Univ. Ostrav., 1, 5-11, (1993) · Zbl 0849.54036
[28] Infante, G; Pietramala, P, Perturbed Hammerstein integral inclusions with solutions that change sign, Comment. Math. Univ. Carol., 50, 591-605, (2009) · Zbl 1212.45009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.