This paper is a continuation of the investigations of F-contractions. The aim of this article is to extend the concept of Ćirić type F-contraction in closed ball. We introduce the notion of F-contraction on closed ball and introduced new approach of fixed point theorems for F-contraction on closed ball in a complete metric space. Our results is very useful for the contraction of the mapping only on closed ball instead on the whole space. Some comparative examples are constructed which 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.
T. Abdeljawad, Meir-Keeler contractive xed and common xed point theorems, Fixed PoinTheory Appl. 2013 doi:10.1186/1687-1812-2013-19.
--------------------------------------------------------------------------[3] . Acar and I. Altun, A Fixed Point Theorem for Multivalued Mappings with -Distance, Abstr. Appl. Anal., Volume 2014, Article ID 497092, 5 pages.
------------------------------------------------------------------------[4] M. Arshad , Fahimuddin, A. Shoaib and A. Hussain, Fixed point results for - -locally graphic contraction in dislocated qusai metric spaces, Math Sci., (2014) doi 10.1007/s40096-014-0132, 7 pages.
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 pp.
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 and Appl. 2013 (2013), article ID 638181, 9 pages.
A. Azam, S. Hussain and M. Arshad, Common fixed points of Chatterjea type fuzzy mappings on closed balls, Neural Computing & Applications, (2012) 21 (Suppl 1):S313S317.
A. Azam, M. Waseem, M. Rashid, Fixed point theorems for fuzzy contractive mappings in quasi-pseudo-metric spaces, Fixed Point Theory Appl., 20132013:27.
N. Hussain, M. Arshad, A. Shoaib and Fahimuddin, Common xed point results for -contractions on a metric space endowed with graph, J. Inequal. Appl., (2014) 2014:136.
N. Hussain and P. Salimi, suzuki-wardowski type xed point theorems for -GF-contractions, Taiwanese J. Math., 20 (20) (2014), doi: 10.11650/tjm.18.2014.4462
N. Hussain, E. Karapinar, P. Salimi, P. Vetro, Fixed point results for GmMeir-Keeler contractive and G-(; )-Meir-Keeler contractive mappings, Fixed Point Theory Appl. 2013, 2013:34. ----------------------------------------------------------------------
N. Hussain, S. Al-Mezel and P. Salimi, Fixed points for Alpha-Psi -graphic contractions with application to integral equations, Abstr. Appl. Anal., (2013) Article 575869.
E. Karapinar and B. Samet, Generalized ( Alpha, psi) contractive type mappings and related xed point theorems with applications, Abstr. Appl. Anal., (2012) Article id:793486.
-----------------------------------------------------------------------[23] E. Kryeyszig., Introductory Functional Analysis with Applications, John Wiley & Sons, New York, (Wiley Classics Library Edition) 1989.
G. Minak, A. Halvaci and I. Altun, ·Ciri·c type generalized Fcontractions on complete metric spaces and xed point results, Filomat, 28 (6) (2014), 1143-1151.
NA. Secelean, Iterated function systems consisting of F-contractions, Fixed Point Theory Appl. 2013, Article ID 277 (2013). doi:10.1186/1687-18122013-277.
A. Shoaib, M. Arshad and J. Ahmad, Fixed point results of locally cotractive mappings in ordered quasi-partial metric spaces, The Scientic World Journal, 2013 (2013), Article ID 194897, 8 pp.
B. Samet, C. Vetro and P. Vetro, Fixed point theorems for -contractive type mappings, Nonlinear Anal. 75 (2012) 21542165.
------------------------------------------------------------------------[34] D. Wardowski, Fixed point theory of a new type of contractive mappings in complete metric spaces. Fixed PoinTheory Appl. (2012) Article ID 94.
T. Abdeljawad, Meir-Keeler contractive xed and common xed point theorems, Fixed PoinTheory Appl. 2013 doi:10.1186/1687-1812-2013-19.
--------------------------------------------------------------------------[3] . Acar and I. Altun, A Fixed Point Theorem for Multivalued Mappings with -Distance, Abstr. Appl. Anal., Volume 2014, Article ID 497092, 5 pages.
------------------------------------------------------------------------[4] M. Arshad , Fahimuddin, A. Shoaib and A. Hussain, Fixed point results for - -locally graphic contraction in dislocated qusai metric spaces, Math Sci., (2014) doi 10.1007/s40096-014-0132, 7 pages.
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 pp.
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 and Appl. 2013 (2013), article ID 638181, 9 pages.
A. Azam, S. Hussain and M. Arshad, Common fixed points of Chatterjea type fuzzy mappings on closed balls, Neural Computing & Applications, (2012) 21 (Suppl 1):S313S317.
A. Azam, M. Waseem, M. Rashid, Fixed point theorems for fuzzy contractive mappings in quasi-pseudo-metric spaces, Fixed Point Theory Appl., 20132013:27.
N. Hussain, M. Arshad, A. Shoaib and Fahimuddin, Common xed point results for -contractions on a metric space endowed with graph, J. Inequal. Appl., (2014) 2014:136.
N. Hussain and P. Salimi, suzuki-wardowski type xed point theorems for -GF-contractions, Taiwanese J. Math., 20 (20) (2014), doi: 10.11650/tjm.18.2014.4462
N. Hussain, E. Karapinar, P. Salimi, P. Vetro, Fixed point results for GmMeir-Keeler contractive and G-(; )-Meir-Keeler contractive mappings, Fixed Point Theory Appl. 2013, 2013:34. ----------------------------------------------------------------------
N. Hussain, S. Al-Mezel and P. Salimi, Fixed points for Alpha-Psi -graphic contractions with application to integral equations, Abstr. Appl. Anal., (2013) Article 575869.
E. Karapinar and B. Samet, Generalized ( Alpha, psi) contractive type mappings and related xed point theorems with applications, Abstr. Appl. Anal., (2012) Article id:793486.
-----------------------------------------------------------------------[23] E. Kryeyszig., Introductory Functional Analysis with Applications, John Wiley & Sons, New York, (Wiley Classics Library Edition) 1989.
G. Minak, A. Halvaci and I. Altun, ·Ciri·c type generalized Fcontractions on complete metric spaces and xed point results, Filomat, 28 (6) (2014), 1143-1151.
NA. Secelean, Iterated function systems consisting of F-contractions, Fixed Point Theory Appl. 2013, Article ID 277 (2013). doi:10.1186/1687-18122013-277.
A. Shoaib, M. Arshad and J. Ahmad, Fixed point results of locally cotractive mappings in ordered quasi-partial metric spaces, The Scientic World Journal, 2013 (2013), Article ID 194897, 8 pp.
B. Samet, C. Vetro and P. Vetro, Fixed point theorems for -contractive type mappings, Nonlinear Anal. 75 (2012) 21542165.
------------------------------------------------------------------------[34] D. Wardowski, Fixed point theory of a new type of contractive mappings in complete metric spaces. Fixed PoinTheory Appl. (2012) Article ID 94.
Hussain, A., Arshad, M., & Nazim, M. (2017). CONNECTION OF CIRIC TYPE F-CONTRACTION INVOLVING FIXED POINT ON CLOSED BALL. Gazi University Journal of Science, 30(1), 283-291.
AMA
Hussain A, Arshad M, Nazim M. CONNECTION OF CIRIC TYPE F-CONTRACTION INVOLVING FIXED POINT ON CLOSED BALL. Gazi University Journal of Science. March 2017;30(1):283-291.
Chicago
Hussain, Aftab, Muhammad Arshad, and Muhammad Nazim. “CONNECTION OF CIRIC TYPE F-CONTRACTION INVOLVING FIXED POINT ON CLOSED BALL”. Gazi University Journal of Science 30, no. 1 (March 2017): 283-91.
EndNote
Hussain A, Arshad M, Nazim M (March 1, 2017) CONNECTION OF CIRIC TYPE F-CONTRACTION INVOLVING FIXED POINT ON CLOSED BALL. Gazi University Journal of Science 30 1 283–291.
IEEE
A. Hussain, M. Arshad, and M. Nazim, “CONNECTION OF CIRIC TYPE F-CONTRACTION INVOLVING FIXED POINT ON CLOSED BALL”, Gazi University Journal of Science, vol. 30, no. 1, pp. 283–291, 2017.
ISNAD
Hussain, Aftab et al. “CONNECTION OF CIRIC TYPE F-CONTRACTION INVOLVING FIXED POINT ON CLOSED BALL”. Gazi University Journal of Science 30/1 (March 2017), 283-291.
JAMA
Hussain A, Arshad M, Nazim M. CONNECTION OF CIRIC TYPE F-CONTRACTION INVOLVING FIXED POINT ON CLOSED BALL. Gazi University Journal of Science. 2017;30:283–291.
MLA
Hussain, Aftab et al. “CONNECTION OF CIRIC TYPE F-CONTRACTION INVOLVING FIXED POINT ON CLOSED BALL”. Gazi University Journal of Science, vol. 30, no. 1, 2017, pp. 283-91.
Vancouver
Hussain A, Arshad M, Nazim M. CONNECTION OF CIRIC TYPE F-CONTRACTION INVOLVING FIXED POINT ON CLOSED BALL. Gazi University Journal of Science. 2017;30(1):283-91.