Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
Open Access
Journal Browser
Go
Turkish Journal of Analysis and Number Theory. 2018, 6(2), 43-48
DOI: 10.12691/tjant-6-2-2
Open AccessArticle

Generalized Dynamic Process for Generalized Multivalued F-contraction of Hardy Rogers Type in b-metric Spaces

Abdullah Shoaib1, , Awais Asif2, Muhammad Arshad2 and Eskandar Ameer2

1Department of Mathematics and Statistics, Riphah International University, Islamabad - 44000, Pakistan

2Department of Mathematics, International Islamic University, H-10, Islamabad 44000, Pakistan

Pub. Date: April 30, 2018

Cite this paper:
Abdullah Shoaib, Awais Asif, Muhammad Arshad and Eskandar Ameer. Generalized Dynamic Process for Generalized Multivalued F-contraction of Hardy Rogers Type in b-metric Spaces. Turkish Journal of Analysis and Number Theory. 2018; 6(2):43-48. doi: 10.12691/tjant-6-2-2

Abstract

The aim of this paper is to establish common fixed point results for multivalued mappings satisfying generalized F-contractive conditions of Hardy Rogers type with respect to generalized dynamic process in b-metric space. Our results improve and generalize several well known results in the existing literature.

Keywords:
fixed point generalized F-contraction b-metric space generalized dynamic process Hausdorff metric

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  M. Abbas, B. Ali and S. Romaguera, Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory and Applications 2013, 2013: 243.
 
[2]  I. Altun, G. Durmaz, Some fixed point theorems on ordered cone metric spaces, Rendiconti del Circolo Matematico di Palermo 58 (2009) 319-325.
 
[3]  M. Arshad, M. Abbas, A. Hussain and N. Hussain, Generalized Dynamic Process for Generalized (f,L)-almost F-Contraction with Applications, J. Nonlinear Sci. Appl. 9 (2016), 1702-1715.
 
[4]  M. Arshad, E. Ameer and A.Hussain, Hardy-Rogers-Type Fixed Point Theorems for α-GF-Contractions, Archivum Mathematicum (BRNO) Tomus 51 (2015), 129-141.
 
[5]  M. Arshad, A. Shoaib, I. Beg, Fixed point of a pair of contractive dominated mappings on a closed ball in an ordered complete dislocated metric space, Fixed Point Theory and Appl. (2013), 2013:115, 15 pages.
 
[6]  M. Arshad, A. Shoaib, and P. Vetro, Common Fixed Points of a Pair of Hardy Rogers Type Mappings on a Closed Ball in Ordered Dislocated Metric Spaces, Journal of Function Spaces, 2013 (2013), Article ID 63818.
 
[7]  M. Arshad , A. Shoaib, M. Abbas and A. Azam, Fixed Points of a pair of Kannan Type Mappings on a Closed Ball in Ordered Partial Metric Spaces, Miskolc Mathematical Notes, 14(3), 2013, 769-784.
 
[8]  M. Arshad, A. Azam, M. Abbas and A. Shoaib, Fixed point results of dominated mappings on a closed ball in ordered partial metric spaces without continuity U.P.B. Sci. Bull., Series A, 76(2), 2014.
 
[9]  A. Azam, M. Arshad, I. Beg, Common fixed points of two maps in cone metric spaces, Rendiconti del Circolo Matematico di Palermo 57 (2008) 433-441.
 
[10]  I.A. Bakhtin, The contraction mapping principle in quasi-metric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst. 30 (1989), 26-37.
 
[11]  I. Beg, M. Arshad , A. Shoaib, Fixed Point on a Closed Ball in ordered dislocated Metric Space, Fixed Point Theory, 16(2), 2015.
 
[12]  V. Berinde, F. Vetro, Common fixed points of mappings satisfying implicit contractive conditions, Fixed Point Theory and Applications 2012:105 (2012).
 
[13]  V. Berinde, F. Vetro, Fixed point for cyclic weak (Ψ, C)-contractions in 0-complete partial metric spaces, Filomat 27 (2013) 1405-1413.
 
[14]  A. Bhatt and H. Chandra, Common fixed points for JH operators and occasionally weakly g-biased pairs under relaxed condition on probabilistic metric space, Journal of Function Spaces and Applications, vol. 2013, Article ID 846315, 6 pages, 2013.
 
[15]  M. Boriceanu, Fixed Point theory for multivalued generalized contraction on a set with two b-metrics, studia Univ Babes, Bolya: Math. LIV (3) (2009), 1-14.
 
[16]  M. Cosentino, P. Vetro, Fixed Point Results for F-Contractive Mappings of Hardy-Rogers-Type, Filomat 28:4 (2014), 715-722.
 
[17]  N. Hussain, J. Ahmad and A. Azam, Generalized fixed point theorems for multi-valued α - ψ -contractive mappings, J. Inequal. Appl., 2014, 2014:348.
 
[18]  N. Hussain, S. Al-Mezel and P. Salimi, Fixed points for ψ -graphic contractions with application to integral equations, Abstract and Applied Analysis, Volume 2013, Article ID 575869.
 
[19]  N. Hussain, M. Arshad, A. Shoaib and Fahimuddin, Common Fixed Point results for α - ψ -contractions on a metric space endowed with graph, J. Inequalities and Appl., 2014, 2014:136.
 
[20]  M. Jleli, H. Kumar, B. Samet and C. Vetro, On multivalued weakly Picard operators in partial Hausdorff metric spaces, Fixed Point Theory and Applications 2015, 2015: 52.
 
[21]  Z. Kadelburg, L. Paunović, S. Radenović, A note on fixed point theorems for weakly T-Kannan and weakly T-Chatterjea contractions in b-metric spaces, Gulf Journal of Mathematics 3 (2015) 57-67.
 
[22]  D. Klim and D. Wardowski, Fixed points of dynamic processes of set-valued F-contractions and application to functional equations, Fixed Point Theory and Applications (2015) 2015: 22.
 
[23]  P. Kumar, M. S. Sachdeva and S. K. Banerjee, Some Fixed Point Theorems in b-metric Space, Turkish Journal of Analysis and Number Theory, 2014, 2(1), 19-22.
 
[24]  A. Shoaib, M. Arshad and J. Ahmad, Fixed point results of locally cotractive mappings in ordered quasi-partial metric spaces, The Scientific World Journal, 2013 (2013), Article ID 194897, 8 pages.
 
[25]  A. Shoaib, M. Arshad and M. A. Kutbi, Common fixed points of a pair of Hardy Rogers Type Mappings on a Closed Ball in Ordered Partial Metric Spaces, J. Comput. Anal. Appl., 17(2014), 255-264.
 
[26]  A. Shoaib, α-η Dominated Mappings and Related Common Fixed Point Results in Closed Ball, Journal of Concrete and Applicable Mathematics, 13(1-2), 2015, 152-170.
 
[27]  N. Shobkolaei, S. Sedghi, J. R. Roshan, andN.Hussain, Suzuki type fixed point results in metric-like spaces, Journal of Function Spaces and Applications, vol. 2013, Article ID 143686, 9 pages, 2013.
 
[28]  S. Shukla, S. Radenović, C. Vetro, Set-valued Hardy-Rogers type contraction in 0-complete partial metric spaces, International Journal of Mathematics and Mathematical Sciences, Volume 2014, Article ID 652925, 9 pages.
 
[29]  S. Shukla, S. Radenović, Z. Kadelburg, Some fixed point theorems for F-generalized contractions in 0-orbitally complete partial metric spaces, Theory and Applications of Mathematics and Computer Science 4(1) (2014) 87-98.
 
[30]  D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory and Appl. 2012:94 (2012).