Fixed point results for multivalued contractive type maps
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Authors
Saleh Abdullah Al-Mezel
- Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia.
Abstract
Using generalized distance in metric spaces, we prove some fixed point results for multivalued generalized
contractive type maps. Consequently, several known fixed point results are either improved or generalized.
An interesting example in support of the result is also presented.
Share and Cite
ISRP Style
Saleh Abdullah Al-Mezel, Fixed point results for multivalued contractive type maps, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 3, 1373--1381
AMA Style
Al-Mezel Saleh Abdullah, Fixed point results for multivalued contractive type maps. J. Nonlinear Sci. Appl. (2016); 9(3):1373--1381
Chicago/Turabian Style
Al-Mezel, Saleh Abdullah. "Fixed point results for multivalued contractive type maps." Journal of Nonlinear Sciences and Applications, 9, no. 3 (2016): 1373--1381
Keywords
- Metric space
- fixed point
- contractive multi-valued map
- w-distance
- u-distance.
MSC
References
-
[1]
S. Banach, Sur les oprations dans les ensembles abstraits et leur application aux quations intgrales, Fund. Math., 3 (1922), 133-181.
-
[2]
B. A. Bin Dehaish, A. Latif , Fixed point results for multivalued contractive maps , Fixed Point Theory Appl., 2012 (2012), 9 pages.
-
[3]
B. A. Bin Dehaish, A. Latif, Fixed point theorems for generalized contractive type multivalued maps, Fixed Point Theory Appl., 2012 (2012), 9 pages.
-
[4]
L. Ciric , Fixed point theorems for multi-valued contractions in metric spaces , J. Math. Anal. Appl., 348 (2008), 499-507.
-
[5]
Y. Feng, S. Liu, Fixed point theorems for multivalued contractive mappings and multivalued Caristi Type mappings, J. Math. Anal. Appl., 317 (2006), 103-112.
-
[6]
S. Hirunworkakit, N. Petrot, Some fixed point theorem for contractive multi-valued mappings induced by generalized distance in metric spaces, Fixed Point Theory Appl., 2011 (2011), 10 pages.
-
[7]
O. Kada, T. Susuki, W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon, 44 (1996), 381-391.
-
[8]
D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces , J. Math. Anal. Appl., 334 (2007), 132-139.
-
[9]
A. Latif, A. A. N. Abdou , Fixed points of generalized contractive maps, Fixed Point Theory Appl., 2009 (2009), 9 pages.
-
[10]
A. Latif, A. A. N. Abdou, Fixed points results for generalized contractive multimaps in metric spaces, Fixed Point Theory Appl., 2009 (2009), 16 pages.
-
[11]
A. Latif, W. A. Albar, Fixed point results in complete metric spaces, Demonstratio Math., 41 (2008), 145-150.
-
[12]
L. J. Lin, W. S. Du, Some equivalent formulations of the generalized Ekland's variational principle and their applications, Nonlinear Anal., 67 (2007), 187-199.
-
[13]
S. B. Nadler, Multivalued contraction mappings , Pacific J. Math. , 30 (1969), 475-488.
-
[14]
T. Suzuki , Generalized distance and existence theorems in complete metric spaces, J. Math. Anal. Appl., 253 (2001), 440-458.
-
[15]
T. Suzuki, W. Takahashi, Fixed point Theorems and characterizations of metric completeness, Topol. Methods Nonlinear Anal., 8 (1996), 371-382.
-
[16]
W. Takahashi, Nonlinear Functional Analysis, Fixed point theory and its applications, Yokohama Publishers (2000)
-
[17]
J. S. Ume, Existence theorems for generalized distance on complete metric space, Fixed Point Theory Appl., 2010 (2010), 21 pages.
-
[18]
J. S. Ume, Fixed point theorems for Kannan-type maps, Fixed Point Theory Appl., 2015 (2015), 13 pages.
-
[19]
J. S. Ume, B. S. Lee, S. J. Cho, Some results on fixed point theorems for multivalued mappings in complete metric spaces, Int. J. Math. Math. Sci., 30 (2002), 319-325.