Search

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.

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 introduce a new concept of generalized cyclic (κh, ϕL)S-weak contraction mappings and establish some coincidence point results for such mappings in complete partially ordered Menger PM-spaces. Our results generalize the main results of Nashine (Nonlinear Anal. 75:6160-6169, 2012) and Gopal et al. (Appl. Math. Comput. 233:955-967, 2014). We also obtain the corresponding coincidence point theorems for generalized cyclic (κh, ϕL)S-weak contractions in partially ordered metric spaces. MSC: 47H10; 54H25

In this paper, the new concepts of generalized Menger probabilistic metric spaces and tripled common fixed point for a pair of mappings T : X × X × X → X and A : X → X are introduced. Utilizing the properties of the pseudo-metric and the triangular norm, some tripled common fixed point problems of hybrid probabilistic contractions with a gauge function φ are studied. The obtained results generalize some coupled common fixed point theorems in the corresponding literature. Finally, an example is given to illustrate our main results. MSC:47H10, 46S50.

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.

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.

In this paper, a new concept of the common property (E.A) for two hybrid pairs of mappings is introduced in Menger PM-spaces. Utilizing this concept, some common fixed point theorems, which shed some new light on the study of fixed point results for hybrid pairs in Menger PM-spaces, are obtained under strict contractive conditions. The corresponding results in metric spaces which generalize many known results are also obtained. Finally, an example is also given to exemplify our main results.