TY - JOUR
ID - 111628
TI - Fixed Point of Multivalued Mizoguchi-Takahashi's Type Mappings and Answer to the Rouhani-Moradi's Open Problem
JO - Mathematics Interdisciplinary Research
JA - MIR
LA - en
SN - 2538-3639
AU - Moradi, Sirous
AU - Fathi, Zahra
AD - Department of Mathematics, Faculty of Sciences, Lorestan University, Khorramabad 68151-4-4316, Iran
AD - Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
Y1 - 2021
PY - 2021
VL - 6
IS - 3
SP - 185
EP - 194
KW - fixed point
KW - Mizoguchi-Takahashi fixed point theorem
KW - multi-valued mapping
KW - weak contraction
DO - 10.22052/mir.2021.240213.1227
N2 - The fixed point theorem of Nadler (1966) was extended by Mizoguchi and Takahashi in 1989 and then for multi-valued contraction mappings, the existence of fixed point was demonstrated by Daffer and Kaneko (1995). Their results generalized the Nadler’s theorem. In 2009 Kamran generalized Mizoguchi-Takahashi’s theorem. His theorem improve Klim and Wadowski results (2007), and extended Hicks and Rhoades (1979) fixed point theorem. Recently Rouhani and Moradi (2010) generalized Daffer and Kaneko’s results for two mappings. The results of the current work, extend the previous results given by Kamram (2009), as well as by Rouhani and Moradi (2010), Nadler (1969), Daffer and Kaneko (1995), and Mizoguchi and Takahashi (1986) for tow multi-valued mappings. We also give a positive answer to the Rouhani-Moradi’s open problem.
UR - https://mir.kashanu.ac.ir/article_111628.html
L1 - https://mir.kashanu.ac.ir/article_111628_6092f5d4bd2792c664bd866be5b6928d.pdf
ER -