In this paper, we generalize the algebraic sum ⊕ of Fang. Based on this concept, we prove some common fixed point theorems for three pairs of self-mappings satisfying the common (E.A) property in Menger PGM-spaces. Finally, an example is given to exemplify our main results.

In this paper, we weaken the notion of Ψ of Luong and Thuan, [V. N. Luong, N. X. Thuan, Nonlinear Anal., 74 (2011), 983-992] and prove some new coupled coincidences and coupled common fixed point theorems for mappings having a mixed g-monotone property in partially ordered complete probabilistic metric spaces. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.

In this paper, we introduce the concepts of generalized probabilistically bounded set * and Menger-Hausdorff metric G * in Menger probabilistic G-metric spaces, and prove that ( * , G * , ) is also a Menger probabilistic G-metric space. Utilizing these concepts, we establish some common fixed point theorems for three hybrid pairs of mappings satisfying the common property (E.A) in Menger probabilistic G-metric spaces. Finally, an example is given to exemplify the theorems. MSC: Primary 47H10; secondary 46S10

In this paper, a new concept of the property G * -(E.A) in Menger P GM -spaces is introduced. Based on this, some common fixed point theorems under strict contractive conditions for mappings satisfying the property G * -(E.A) in Menger P GM -spaces and the corresponding results in G-metric spaces are obtained. Finally, an example is given to exemplify our main results.