Let E be a reflexive Banach space with a weakly sequentially continuous duality mapping, C be a nonempty closed convex subset of E, f : C → C a contractive mapping (or a weakly contractive mapping), and T : C → C a nonexpansive mapping with the fixed point set F (T ) 6= ∅. Let {xn} be generated by a new composite iterative scheme: yn = λnf(xn)+(1−λn)Txn, xn+1 = (1−βn)yn+βnTyn, (n ≥ 0). It is pr...

In this paper, we introduce the notion of generalized (α, φ, ψ)- Geraghty contractive type mappings in setup Sb-metric spaces and α-orbital admissible with respect to φ. Furthermore, fixed-point theorems for such complete are proven without assuming subadditivity ψ. Some examples provided supporting our main results. Also, gave an application integral equations as well Homotopy.

This paper analyzes the complexity of the contraction fixed point problem: compute an ε-approximation to the fixed point V ∗ = Γ(V ∗) of a contraction mapping Γ that maps a Banach space Bd of continuous functions of d variables into itself. We focus on quasi linear contractions where Γ is a nonlinear functional of a finite number of conditional expectation operators. This class includes contrac...

Our aim is to present some common fixed point theorems in bipolar metric spaces via certain contractive conditions. Some  examples have been provided to illustrate the effectiveness of new results. At the end, we give two applications dealing with homotopy theory and integral equations.

This paper aims to introduce the new concept of rational type fuzzy-contraction mappings in fuzzy metric spaces. We prove some fixed point results under conditions spaces with illustrative examples support our results. will play a very important role theory and can be generalized for different contractive context Moreover, we present an application nonlinear integral equation get existing resul...