### Invariant approximations, generalized $I$-contractions, and $R$-subweakly commuting maps.

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In this paper we prove a general random fixed point theorem for multivalued maps in Frechet spaces. We apply our main result to obtain some common random fixed point theorems. Our main result unifies and extends the work due to Benavides, Acedo and Xu [4], Itoh [8], Lin [12], Liu [13], Tan and Yuan [20], Xu [23], etc.

Some common fixed point theorems in normed spaces are proved using the concept of biased mappings- a generalization of compatible mappings.

In this paper we extend the concept of $R$-weak commutativity to the setting of single-valued and multivalued mappings. We also establish a coincidence theorem for pairs of $R$-weakly commuting single-valued and multivalued mappings satisfying a contractive type condition.

We provide an answer to a question: under what conditions almost continuity in the sense of Husain implies closure continuity?

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