F-HR-type contractions on (\(\alpha,\eta\))-complete rectangular b-metric spaces
-
2039
Downloads
-
3757
Views
Authors
Nawab Hussain
- Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
Vahid Parvaneh
- Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran.
Badria A. S. Alamri
- Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
Zoran Kadelburg
- Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Beograd, Serbia.
Abstract
The aim of this paper is to present some fixed point results for generalized Wardowski-type contractions in the framework
of (\(\alpha,\eta\))-complete rectangular b-metric spaces. We also derive certain fixed point results for generalized F-contractions in
rectangular b-metric spaces endowed with a graph or a partial order. Moreover, an illustrative example is presented to support
the obtained results.
Share and Cite
ISRP Style
Nawab Hussain, Vahid Parvaneh, Badria A. S. Alamri, Zoran Kadelburg, F-HR-type contractions on (\(\alpha,\eta\))-complete rectangular b-metric spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 3, 1030--1043
AMA Style
Hussain Nawab, Parvaneh Vahid, Alamri Badria A. S., Kadelburg Zoran, F-HR-type contractions on (\(\alpha,\eta\))-complete rectangular b-metric spaces. J. Nonlinear Sci. Appl. (2017); 10(3):1030--1043
Chicago/Turabian Style
Hussain, Nawab, Parvaneh, Vahid, Alamri, Badria A. S., Kadelburg, Zoran. "F-HR-type contractions on (\(\alpha,\eta\))-complete rectangular b-metric spaces." Journal of Nonlinear Sciences and Applications, 10, no. 3 (2017): 1030--1043
Keywords
- b-metric space
- rectangular metric space
- Hardy-Rogers condition
- F-contraction
- admissible mappings
- property P.
MSC
References
-
[1]
I. A. Bakhtin, The contraction mapping principle in almost metric space, (Russian) Functional analysis, Ulyanovsk. Gos. Ped. Inst., Ulyanovsk, (1989), 26–37.
-
[2]
A. Branciari , A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (2000), 31–37.
-
[3]
M. Cosentino, M. Jleli, B. Samet, C. Vetro, Solvability of integrodifferential problems via fixed point theory in b-metric spaces, Fixed Point Theory Appl., 2015 (2015 ), 15 pages.
-
[4]
M. Cosentino, P. Vetro, Fixed point results for F-contractive mappings of Hardy-Rogers-type, Filomat, 28 (2014), 715–722.
-
[5]
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5–11.
-
[6]
S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 263–276.
-
[7]
N. Hussain, M. A. Kutbi, P. Salimi, Fixed point theory in \(\alpha\)-complete metric spaces with applications, Abstr. Appl. Anal., 2014 (2014), 11 pages.
-
[8]
N. Hussain, V. Parvaneh, J. R. Roshan, Fixed point results for \(G-\alpha-\)contractive maps with applications to boundary value problems, Scientific World J., 2014 (2014), 14 pages.
-
[9]
N. Hussain, P. Salimi, Suzuki-Wardowski type fixed point theorems for \(\alpha-GF-\)contractions, Taiwanese J. Math., 18 (2014), 1879–1895.
-
[10]
J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136 (2008), 1359–1373.
-
[11]
G. S. Jeong, B. E. Rhoades, Maps for which \(F(T) = F(T^n)\), Fixed Point Theory applications, Vol. 6, 71–105, Nova Sci. Publ., New York (2007)
-
[12]
M. Jleli, B. Samet, C. Vetro, F. Vetro, Fixed points for multivalued mappings in b-metric spaces, Abstr. Appl. Anal., 2015 (2015 ), 7 pages.
-
[13]
Z. Kadelburg, S. Radenović, On generalized metric spaces: a survey, TWMS J. Pure Appl. Math., 5 (2014), 3–13.
-
[14]
M. A. Kutbi, A. Alam, M. Imdad, Sharpening some core theorems of Nieto and Rodríguez-López with application to boundary value problem, Fixed Point Theory Appl., 2015 (2015), 15 pages.
-
[15]
V. La Rosa, P. Vetro, Common fixed points for \(\alpha-\psi-\phi\)-contractions in generalized metric spaces, Nonlinear Anal. Model. Control, 19 (2014), 43–54.
-
[16]
J. J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223–229.
-
[17]
J. R. Roshan, V. Parvaneh, Z. Kadelburg, N. Hussain, New fixed point results in b-rectangular metric spaces, Nonlinear Anal. Model. Control, 21 (2016), 614–634.
-
[18]
B. Samet, Discussion on ''A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces'' by A. Branciari, Publ. Math. Debrecen, 76 (2010), 493–494.
-
[19]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha -\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154–2165.
-
[20]
I. R. Sarma, J. M. Rao, S. S. Rao , Contractions over generalized metric spaces, J. Nonlinear Sci. Appl., 2 (2009), 180–182.
-
[21]
T. Suzuki, Generalized metric spaces do not have the compatible topology, Abstr. Appl. Anal., 2014 (2014), 5 pages.
-
[22]
T. Van An, N. Van Dung, Z. Kadelburg, S. Radenović, Various generalizations of metric spaces and fixed point theorems, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 109 (2015), 175–198.
-
[23]
F. Vetro, F-contractions of Hardy-Rogers type and application to multistage decision processes, Nonlinear Anal. Model. Control, 21 (2016), 531–546.
-
[24]
D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012 ), 6 pages.