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In this paper, we introduce the new concepts of multidimensional Menger probabilistic metric spaces and related fixed point for a pair of mappings T: $\underbrace{X\times X\times\cdots\times X}_{n}\rightarrow X $ and A: $X\rightarrow X$. Utilizing the properties of the related triangular norm and the compatibility of A with T, some multidimensional common fixed point problems of hybrid probabilistic contractions with a gauge function φ are studied. The obtained results generalize some coupled and triple common fixed point theorems in the corresponding literature. Finally, an example is given to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of generalized probabilistically bounded set $\Omega^{*}$ and Menger-Hausdorff metric $\widetilde{G}^{*}$ in Menger probabilistic G-metric spaces, and prove that $(\Omega^{*},\widetilde{G}^{*},\Delta)$ 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this work, we introduce a new φ-contractive mapping; following that, we obtain some multipled common fixed point theorems for a pair of mappings $T: \underbrace{X \times X \times\cdots\times X}_{m\text{-times}}\rightarrow X$ and $A: X\rightarrow X$. The main results of this paper are generalization of the main results of Kutbi et al. (Fixed Point Theory Appl. 2015(1):32, 2015). As an illustration, we give an example to demonstrate the validity of the obtained results. [ABSTRACT FROM AUTHOR]

Abstract The aim of this paper is to propose a new φ -coupled fixed point theorem for a mixed monotone mapping in a metric space, which is taken no account of the continuity of the mapping. To this end, we introduce the notions of φ -coupled fixed point and modified F -control function. Our obtained results are applied to derive some φ -coupled fixed point theorems in partial metric spaces and quasi-metric spaces, respectively. Some applications to matrix equations and integral equations are also presented so as to illustrate our results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, some new theorems for various cyclic contractions are established in G b -metric spaces to discuss the existence and uniqueness of the solutions for a class of the operator equations, which generalize many known results in corresponding literatures. On the other hand, we introduce the notion of the cyclic α - ψ φ-contractive mappings in G b -metric spaces and establish a new fixed point theorem, which is applied to consider the existence of the solutions of the integral equations and ordinary differential equations. Moreover, some examples are given to support our main results. [ABSTRACT FROM AUTHOR]