New common fixed point theorems for multivalued maps

S.L. Singh, Raj Kamal, Renu Chugh, Swami Nath Mishra

Abstract

Common fixed point theorems for a new class of multivalued maps are obtained, which generalize and extend classical fixed point theorems of Nadler and Reich and some recent Suzuki type fixed point theorems.

Keywords

Fixed point; Banach contraction theorem; Hausdorff metric space

Subject classification

54H25; 47H10.

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References

A. Abkar and M. Eslamian, Fixed point theorems for Suzuki generalized nonexpansive multivalued mappings in Banach spaces, Fixed Point Theory Appl. 2010 (2010), 10 pp.

(http://dx.doi.org/10.1155/2010/457935)

N. A. Assad and W. A. Kirk, Fixed point theorems for set-valued mappings of contractive type, Pacific J. Math. 43 (1972), 553-562.

(http://dx.doi.org/10.2140/pjm.1972.43.553)

Lj. B. Ciric, Fixed points for generalized multivalued contractions, Mat. Vesnik 9, no. 24 (1972), 265-272.

Lj. B. Ciric, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc. 45 (1974), 267-273.

(http://dx.doi.org/10.2307/2040075)

B. Damjanovic and D. Doric, Multivalued generalizations of the Kannan fixed point

theorem, Filomat 25, no. 1 (2011),125-131.

(http://dx.doi.org/10.2298/FIL1101125D)

S. Dhompongsa and H. Yingtaweesittikul, Fixed points for multivalued mappings and the metric completeness, Fixed Point Theory Appl. 2009 (2009), 15 pp.

(http://dx.doi.org/10.1155/2009/972395)

D. Doric and R. Lazovic, Some Suzuki-type fixed point theorems for generalized

multivalued mappings and applications, Fixed Point Theory Appl. 2011 (2011), 13 pp.

(http://dx.doi.org/10.1186/1687-1812-2011-40)

M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal. 69, no. 9 (2008), 2942-2949.

(http://dx.doi.org/10.1016/j.na.2007.08.064)

M. Kikkawa and T. Suzuki, Some notes on fixed point theorems with constants, Bull. Kyushu Inst. Technol. Pure Appl. Math. 56 (2009), 11-18.

G. Mot and A. Petrusel, Fixed point theory for a new type of contractive multi-valued operators, Nonlinear Anal. 70, no. 9 (2008), 3371-3377.

(http://dx.doi.org/10.1016/j.na.2008.05.005)

S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475-488.

(http://dx.doi.org/10.2140/pjm.1969.30.475)

S. B. Nadler, Hyperspaces of Sets, Marcel Dekker, New York, 1978.

O. Popescu, Two fixed point theorems for generalized contractions with constants in complete metric space, Cent. Eur. J. Math. 7, no. 3 (2009), 529-538.

(http://dx.doi.org/10.2478/s11533-009-0019-2)

S. Reich, Fixed points of multi-valued functions. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 51, no. 8 (1971), 32-35.

B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-290.

(http://dx.doi.org/10.1090/S0002-9947-1977-0433430-4)

B. D. Rouhani and S. Moradi, Common fixed point of multivalued generalized $varphi$-weak contractive mappings, Fixed Point Theory Appl. 2010 (2010), Art. ID 708984, 13 pp.

I. A. Rus, Fixed point theorems for multivalued mappings in complete metric spaces, Math. Japon. 20 (1975), 21-24.

I. A. Rus, Generalized Contractions And Applications, Cluj-Napoca, 2001.

K. P. R. Sastry and S. V. R. Naidu, Fixed point theorems for generalized contraction mappings, Yokohama Math. J. 25 (1980), 15-29.

S. L. Singh and S. N. Mishra, Coincidence theorems for certain classes of hybrid contractions, Fixed Point Theory Appl. 2010 (2010), 14 pp.

(http://dx.doi.org/10.1155/2010/898109)

S. L. Singh and S. N. Mishra, Remarks on recent fixed point theorems, Fixed Point Theory Appl. 2010 (2010), 18 pp.

(http://dx.doi.org/10.1155/2010/452905)

S. L. Singh and S. N. Mishra, Fixed point theorems for single-valued and multi-valued maps. Nonlinear Anal. 74, no. 6 (2011), 2243-2248.

(http://dx.doi.org/10.1016/j.na.2010.11.029)

T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (5) (2008), 1861-1869.

(http://dx.doi.org/10.1090/S0002-9939-07-09055-7)

T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal. 71, no. 11 (2009), 5313-5317.

(http://dx.doi.org/10.1016/j.na.2009.04.017)

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