Fixed point results for multivalued contractive maps

Abstract

Using the concept of u-distance, we prove a fixed point theorem for multivalued contractive maps. We also establish a multivalued version of the Caristi's fixed point theorem and common fixed point result. Consequently, several known fixed point results are either improved or generalized including the corresponding fixed point results of Caristi, Mizoguchi-Takahashi, Kada et al., Suzuki-Takahashi, Suzuki, and Ume. Mathematics Subject Classification (2000): 47H10; 54H25.

Feng-Liu Type Fixed Point Results for Multivalued Mappings in GMMS

“…The second, a generalization of a result of Edelstein, is a fixed point theorem for compact set-valued local contractions. Nadler's study is applied through other metric spaces, such as in [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

The Existence of Fixed Point Theorems via -Distance and -Admissible Mappings and Applications

“…In fact, this result is an improvement of the Nadler's fixed point theorem. Several fixed point theorems have been proved by many mathematicians in framework of metric spaces viadistance; for example, see [16][17][18][19]. Recently, Kutbi [20] established useful lemma for -distance which is an improved version of the lemma given in [21] and proved a key lemma on the existence of -orbit for generalized -contraction mappings.…”

Fixed point results for multivalued contractive type maps

“…Recently, Ume [17] generalized the notion of τ -distance by introducing a concept of u-distance in metric spaces. Several interesting fixed point results have been studied and generalized with respect to u-distance; see [2,3,12,17,18].…”

“…Motivated by the work in [2,3,17], we prove some fixed point results for multivalued contractive type maps induced by the generalized distance in metric spaces. Our results unify and generalize many known fixed point results including the well-known corresponding fixed point results of Ciric [4], Klim and Wardowski [8], Latif and Abdou [10].…”