Fixed point theorems for non-self mappings with nonlinear contractive condition in strictly convex Menger PM-spaces

Nikolić, Rale M.; Ješić, Siniša N.; Babačev, Nataša A.

doi:10.24193/fpt-ro.2017.1.25

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“…The first result from the fixed point theory in probabilistic metric spaces was obtained by Sehgal and Bharucha-Reid [15]. Since then, the fixed and common fixed point theorems for various contraction mappings in probabilistic metric spaces were investigated by many authors (see e.g., [16][17][18][19][20][21][22][23]).…”

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confidence: 99%

Common Fixed Points Theorems for Self-Mappings in Menger PM-Spaces

Nikolić

Pant²,

Ristić

et al. 2022

Mathematics

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The purpose of this paper is to prove that orbital continuity for a pair of self-mappings is a necessary and sufficient condition for the existence and uniqueness of a common fixed point for these mappings defined on Menger PM-spaces with a nonlinear contractive condition. The main results are obtained using the notion of R-weakly commutativity of type Af (or type Ag). These results generalize some known results.

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