Common fixed point theorems for self-mappings in Menger PM-spaces with nonlinear contractive condition

Ješić, Siniša N.; Nikolić, Rale M.; Pant, Neeraj

doi:10.1007/s11784-018-0569-7

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Cited by 2 publications

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“…Proving whether Theorems 2 and 3 remain true if we replace R-weakly commutativity of type A f (or type A g ) with some other concept of commutativity of two self-mappings in the weaker sense. A positive answer for Theorem 2 in this sense was obtained by Ješić et al [19] for a pair of semi R-commuting mappings;…”

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confidence: 93%

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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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confidence: 93%

“…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]).…”

Section: Introductionmentioning

confidence: 99%