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A general fixed point theorem for hybrid pairs of mappings satisfying a new type of limit range property

Popa V., Patriciu A.-M.

Fasciculi Mathematici

2018

Nr 61

143--162

In this paper a new type of common limit range property is introduced, which generalizes the notion of strongly tangential property [9] and joint common limit range property [16]. A general fixed point theorem for two pairs of hybrid mappings involving altering distance and satisfying an implicit relation is proved, generalizing the results from [9], [16] and other papers. As application, we obtain new results for contractive mappings satisfying a contractive condition of integral type, for mappings satisfying ф - contractive conditions and satisfying (ψ, ф) - contractive conditions.

A general coincidence and fixed point theorem for hybrid pairs of mappings satisfying a common coincidence range property

Popa V., Patriciu A.-M.

Fasciculi Mathematici

2017

Nr 58

145--154

In this paper the notion of common coincidence range property is introduced and a general coincidence and fixed point theorem is proved. As applications, new results for mappings satisfying a contractive condition of integral type and for mappings satisfying a φ-contractive condition are obtained.