Common Fixed Point Theorems for a Finite Family of Discontinuous and Noncommutative Maps

Abstract

We study common fixed point theorems for a finite family of discontinuous and noncommutative single-valued functions defined in complete metric spaces. We also study a common fixed point theorem for two multivalued self-mappings and a stationary point theorem in complete metric spaces. Throughout this paper, we establish common fixed point theorems without commuting and continuity assumptions. In contrast, commuting or continuity assumptions are often assumed in common fixed point theorems. We also give examples to show our results. Results in this paper except those that generalized Banach contraction principle and those improve and generalize recent results in fixed point theorem are original and different from any existence result in the literature. The results in this paper will have some applications in nonlinear analysis and fixed point theory.

Common Fixed Point Theorem for Multi-Valued Mappings on B-Metric Spaces

“…The study of a common fixed point for multi-valued mappings has been widely developed and extended by the following researchers. On complete metric space, Lia-Jiu Lin and Sung-Yu Wang [8] have proved the theorem.…”

Common Fixed Point Results of Set Valued Maps for Aφ-Contraction and Generalized ϕ-Type Weak Contraction

“…There have been enormous developments in the area of existence and uniqueness of fixed point for multi valued and set valued mappings in various directions-see [5][6][7][8][9][10][11][12][13][14][15][16]. Some references that have been instrumental for the current work are [17][18][19][20][21][22][23][24][25][26][27].…”

Perov multivalued contraction pair in rectangular cone metric spaces

“…He showed that a multivalued contraction possesses a fixed point in a complete metric space. Later several generalizations of Nadler's fixed point theorem were obtained (see, [27,28]).…”