New type of multivalued F-contraction involving fixed points on closed ball

Volume 17, Issue 2, pp 246-254 http://dx.doi.org/10.22436/jmcs.017.02.06

Publication Date: June 15, 2017 Submission Date: June 07, 2016

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Authors

Aftab Hussain - Department of Mathematical Sciences, Lahore Leads University, Lahore - 54000, Pakistan. Hafiz Farooq Ahmad - College of Computer Sciences and Information Technology (CCSIT) King Faisal University, Alahssa 31982, Kingdom of Saudi Arabia. Muhammad Arshad - Department of Mathematics, International Islamic University, H-10, Islamabad - 44000, Pakistan. Muhammad Nazam - Department of Mathematics, International Islamic University, H-10, Islamabad - 44000, Pakistan.

Abstract

This paper is a continuation of the investigations of F-contraction. The aim of this article is to extend the concept of F-contraction on closed ball. We introduce the notion of Ćirić type multivalued F-contraction on closed ball and establish new fixed point theorems for Ćirić type multivalued F-contraction on closed ball in a complete metric space. Our results are very useful for the contraction of the mapping only on closed ball instead on the whole space. Some comparative examples are constructed whose illustrate the superiority of our results. Our results provide extension as well as substantial generalizations and improvements of several well-known results in the existing comparable literature.

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Keywords

• Metric space
• fixed point
• F-contraction
• closed ball.

MSC

•  46S40
•  47H10
•  54H25

References

• [1] M. Abbas, B. Ali, S. Romaguera, Fixed and periodic points of generalized contractions in metric spaces , Fixed Point Theory Appl., 2013 (2013 ), 11 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [2] M. Abbas, T. Nazir, T. A. Lampert, S. Radenović, Common fixed points of set-valued F-contraction mappings on domain of sets endowed with directed graph , Comp. Appl. Math., 36 (2017), 1607–1622
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] T. Abdeljawad, Meir-Keeler \(\alpha\)-contractive fixed and common fixed point theorems, Fixed PoinTheory Appl., 2013 (2013 ), 10 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] Ö . Acar, I. Altun, A fixed point theorem for multivalued mappings with \(\delta\)-distance, Abstr. Appl. Anal., 2014 (2014 ), 5 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [5] Ö. Acar, G. Durmaz, G. Minak, Generalized multivalued F-contractions on complete metric spaces , Bull. Iranian Math. Soc., 40 (2014), 1469–1478.
  • MathSciNet
  • Google Scholar


• [6] H. H. Alsulami, E. Karapınar, H. Piri, Fixed points of generalized F-Suzuki type contraction in complete b-metric spaces, Discrete Dyn. Nat. Soc., 2015 (2015 ), 8 pages.
  • View Article
  • MathSciNet


• [7] M. Arshad, E. Ameer, A. Hussain, Hardy-Rogers-type fixed point theorems for \(\alpha-GF\)-contractions , Arch. Math. (Brno), 51 (2015), 129–141.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] M. Arshad, Fahimuddin, A. Shoaib, A. Hussain, Fixed point results for \(\alpha-\psi\)-locally graphic contraction in dislocated qusai metric spaces, [[Corrected title: Fixed point results for \(\alpha-\psi\)-locally graphic contraction in dislocated quasi metric spaces]] Math. Sci. (Springer), 8 (2014), 79–85.
  • View Article
  • MathSciNet
  • Google Scholar


• [9] M. Arshad, A. Shoaib, I. Beg, Fixed point of a pair of contractive dominated mappings on a closed ball in an ordered dislocated metric space, Fixed Point Theory Appl., 2013 (2013 ), 15 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] M. Arshad, A. Shoaib, P. Vetro, Common fixed points of a pair of Hardy Rogers type mappings on a closed ball in ordered dislocated metric spaces , J. Funct. Spaces Appl., 2013 (2013 ), 9 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] A. Azam, S. Hussain, M. Arshad, Common fixed points of Chatterjea type fuzzy mappings on closed balls, Neural Comput. Appl., 21 (2012), 313–317.
  • View Article
  • Google Scholar


• [12] A. Azam, M. Waseem, M. Rashid, Fixed point theorems for fuzzy contractive mappings in quasi-pseudo-metric spaces, Fixed Point Theory Appl., 2013 (2013 ), 14 pages.
  • View Article
  • Google Scholar
  • MATH


• [13] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133–181.
  • Google Scholar


• [14] L. B. Ćirić, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc., 45 (1974), 267–273.
  • View Article
  • Google Scholar


• [15] M. Cosentino, P. Vetro, Fixed point results for F-contractive mappings of Hardy-Rogers-type, Filomat, 28 (2014), 715– 722.
  • View Article
  • MathSciNet
  • MATH


• [16] M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 (1962), 74–79.
  • View Article
  • MathSciNet
  • Google Scholar


• [17] B. Fisher, Set-valued mappings on metric spaces , Fund. Math., 112 (1981), 141–145.
  • Google Scholar


• [18] M. A. Geraghty, On contractive mappings, Proc. Amer. Math. Soc., 40 (1973), 604–608.
  • View Article
  • Google Scholar


• [19] N. Hussain, S. Al-Mezel, P. Salimi, Fixed points for \(\psi\)-graphic contractions with application to integral equations, Abstr. Appl. Anal., 2013 (2013 ), 11 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [20] N. Hussain, M. Arshad, M. Abbas, A. Hussain, Generalized dynamic process for generalized (f, L)-almost F-contraction with applications, J. Nonlinear Sci. Appl., 9 (2016), 1702–1715.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [21] A. Hussain, M. Arshad, S. U. Khan, \(\tau\)-Generalization of fixed point results for F-contractions, Bangmod Int. J. Math. Comp. Sci., 1 (2015), 136–146.
  • Google Scholar


• [22] A. Hussain, M. Arshad, M. Nazam, Connection of Ćirić type F-contraction involving fixed point on closed ball, Gazi Univ. J. Sci., (Accepted),
  • Google Scholar


• [23] N. Hussain, M. Arshad, A. Shoaib, Fahimuddin , Common fixed point results for \(\alpha-\psi\)-contractions on a metric space endowed with graph , J. Inequal. Appl., 2014 (2014 ), 14 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [24] N. Hussain, E. Karapınar, P. Salimi, F. Akbar, \(\alpha\)-admissible mappings and related fixed point theorems, J. Inequal. Appl., 2013 (2013 ), 11 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [25] N. Hussain, E. Karapınar, P. Salimi, P. Vetro, Fixed point results for \(G^m\)-Meir-Keeler contractive and \(G-(\alpha,\psi)\)-Meir- Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013 ), 14 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [26] N. Hussain, P. Salimi, Suzuki-Wardowski type fixed point theorems for \(\alpha-GF\)-contractions, Taiwanese J. Math., 18 (2014), 1879–1895.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [27] N. Hussain, P. Salimi, A. Latif, Fixed point results for single and set-valued \(\alpha-\eta-\psi\)-contractive mappings, Fixed Point Theory Appl., 2013 (2013 ), 23 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [28] E. Karapınar, M. A. Kutbi, H. Piri, D. O’Regan, Fixed points of conditionally F-contractions in complete metric-like spaces, Fixed Point Theory Appl., 2015 (2015), 14 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [29] E. Karapınar, B. Samet, Generalized \(\alpha-\psi\) contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal., 2012 (2012 ), 17 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [30] E. Kreyszig, Introductory functional analysis with applications, Wiley Classics Library. John Wiley & Sons, Inc., New York (1989)
  • MathSciNet


• [31] M. A. Kutbi, M. Arshad, A. Hussain, On modified (\(\alpha-\eta\))-contractive mappings, Abstr. Appl. Anal., 2014 (2014 ), 7 pages.


• [32] M. A. Kutbi, M. Arshad, A. Hussain, Fixed point results for Ćirić type \(\alpha-\eta-GF\)-contractions, J. Comput. Anal. Appl., 21 (2016), 466–481.
  • MathSciNet
  • Google Scholar
  • MATH


• [33] M. A. Kutbi, W. Sintunavarat, On new fixed point results for (\(\alpha,\psi,\xi\))-contractive multi-valued mappings on \(\alpha\)-complete metric spaces and their consequences, Fixed Point Theory Appl., 2015 (2015 ), 15 pages.
  • View Article
  • MathSciNet
  • MATH


• [34] G. Mınak, A. Halvacı, I. Altun, Ćirić type generalized F-contractions on complete metric spaces and fixed point results, Filomat, 28 (2014), 1143–1151.
  • View Article
  • MathSciNet
  • MATH


• [35] S. B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475–488.
  • Google Scholar


• [36] H. Piri, P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl., 2014 (2014 ), 11 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [37] P. Salimi, A. Latif, N. Hussain, Modified \(\alpha-\psi\)-contractive mappings with applications , Fixed Point Theory Appl., 2013 (2013 ), 19 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [38] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154–2165.
  • View Article
  • Google Scholar


• [39] N. A. Secelean, Iterated function systems consisting of F-contractions, Fixed Point Theory Appl., 2013 (2013 ), 13 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [40] M. Sgroi, C. Vetro, Multi-valued F-contractions and the solution of certain functional and integral equations, Filomat, 27 (2013), 1259–1268.
  • View Article
  • MathSciNet
  • MATH


• [41] A. Shoaib, M. Arshad, J. Ahmad, Fixed point results of locally cotractive mappings in ordered quasi-partial metric spaces, Scientific World J., 2013 (2013 ), 8 pages.
  • View Article
  • Google Scholar


• [42] A. Shoaib, A. Hussain, M. Arshad, A. Azam, Fixed point results for \(\alpha_*-\psi\) -Ciric type multivalued mappings on an intersection of a closed ball and a sequence with graph, J. Math. Anal., 7 (2016), 41–50.
  • MathSciNet
  • MATH


• [43] S. Shukla, S. Radenović, Some common fixed point theorems for F-contraction type mappings on 0-complete partial metric spaces, J. Math., 2013 (2013 ), 7 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [44] S. Shukla, S. Radenović, Z. Kadelburg, Some fixed point theorems for ordered F-generalized contractions in 0-f-orbitally complete partial metric spaces, Theory Appl. Math. Comput. Sci., 4 (2014), 87–98.
  • Google Scholar
  • MATH


• [45] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012 ), 6 pages.
  • View Article
  • MathSciNet