A new approach to "Equation missing"-contractive nonself multivalued mappings

Abstract

In this paper, we introduce the notions of α-admissible and α-ψ-contractive type condition for nonself multivalued mappings. We establish fixed point theorems using these new notions along with a new condition. Moreover, we have constructed examples to show that our new condition is different from the corresponding existing conditions in the literature. MSC: 47H10; 54H25

Multivalued F-contractions and related fixed point theorems with an application

“…Semat et al [2] succeeded to generalized Banach contraction condition by introducing α-ψ-contraction. Many authors appreciate these two condition conditions which can be seen in [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In this paper, we combine these two ideas to introduce some new contraction conditions for multivalued mappings and corresponding fixed point theorem.…”

Fixed Point Theorems for Multivalued Mappings Involvingα-Function

“…Ali and Kamran [4] further generalized the notion of * --contractive mappings and obtained some fixed point theorems for multivalued mappings. Related results in this direction are also given in [5][6][7][8][9]. In addition to that, Ali et al [10] introduced the notion of ( , , )contractive multivalued mappings to generalize and extend the notion of --contractive mappings to closed valued multifunctions and proved some fixed point theorems for such mappings in complete metric spaces.…”

On some fixed points of alpha-psi contractive mappings with rational expressions

“…For some other examples concerning the class of α-admissible mappings, we can see [2,3,7,9,19,24]. Definition 1.4.…”