Three fixed point theorems which extended the fixed point theory for Kannan's mappings were proved in [11].
In a separable metric space, random fixed point theorems for contraction mappings were proved by Hans̆ [8, 9], Hans̆ and S̆pac̆ek [10] and Mukherjee [11, 12].
In particular, some useful fixed point theorems for monotone mappings were proved by Zhang [19], Guo and Lakshmikantham [20], and Bhaskar and Lakshmikantham [21] under some weak assumptions.
Afterward, some fixed point results for generalized weak contraction mappings were proved by Choudhury et al. [2] by using some control function along with the notion of an altering distance function.
More recently, in Ghoncheh and Razani [5], the notion of C-condition introduced in [4] was generalized to the case of multi-valued version and some existence theorems of fixed point for these mappings were proved in a Ptolemy metric space.
Strong convergence theorems for approximation of common fixed points of a finite family of pseudocontractive mappings are proven in Banach spaces using an implicit iteration scheme.
In the context of modular function spaces, convergence to fixed points of some iterative algorithms, applied to asymptotic pointwise nonexpansive mappings, was proven by Bin Dehaish and Kozlowski in [22].
In this paper, the PPF dependent fixed point theorems and the PPF dependent coincidence points for a pair of mappings are proven in terms of more general contractive conditions in Banach spaces.
Fixed point theorems for Perov-type α-quasi contraction mapping, Kannan-type contraction as well as Chatterjee-type contraction mappings are proved in a dislocated cone metric space over Banach algebra.
In addition, new results for cyclic mappings are proved.
