The Study Of Manageable Functions And Approximate Fixed Point Property With Their Application

Authors

Farshid Khojasteh - aYoung Researcher and Elite Club, Arak Branch, Islamic Azad University, Arak, Iran
Antonio Francisco Roldan Lopez De Hierro - Department of Mathematics, University of Ja´en, Ja´en, Spain

Abstract

In this work, we want to investigate and improve the concept of manageable functions and M_n (R)-contractions in order to extend the theory of multi-valued contractions and fixed point results

Keywords

Manageable function, Hausdorff metric, α-admissible multi-valued map, regularity, fixed point

References

[1] A. Amini-Harandi, Endpoints of set-valued contractions in metric spaces, Nonlinear Anal., 72 (2010), 132–134
[2] S. Banach, Sur les op´erations dans les ensembles abstraits et leurs applications aux ´equations int´egrales, Fund. Math., 3 (1922), 133–181
[3] M. Berinde, V. Berinde, On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl., 326 (2007), 772–782
[4] Lj. B. Ciri´c, ´ contraction and fixed point theorems, Publ. Inst. Math., 12 (1971), 19–26
[5] S. Reich, Fixed points of contractive functions, Boll. Un. Mat. Ital., 5 (1972), 26–42
[6] P. Z. Daffer, H. Kaneko, Fixed points of generalized contractive multi-valued mappings, J. Math. Anal. Appl., 192 (1995), 655—666
[7] W. S. Du, On coincidence point and fixed point theorems for nonlinear multivalued maps. Topology Appl. 159 (2012), 49–56
[8] N. Hussain, A. Amini-Harandi, Y. J. Cho, Approximate endpoints for set valued contractions in metric spaces, Fixed Point Theory Appl., 2010 (2010), 13 pages
[9] S. B. Nadler, Multi valued contraction mappings, Pacific J. Math., 30 (1969), 475–488
[10] N. Mizoguchi, W. Takahashi, Fixed-point theorems for multi valued mappings on complete metric spaces, J. Math. Anal. Appl., 141 (1989), 177–188
[11] B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001), 2683–2693
[12] S. Moradi, F. Khoajsteh, Endpoints of multi valued generalized weak contraction mappings, Nonlinear Anal., 74 (2011), 2170–2174
[13] W. S. Du, F. Khojasteh, New Results and Generalizations for Approximate Fixed Point Property and Their Applications, Abstr. Appl. Anal., (2014) 2014, 9 pages