In this paper, the notion of θ*-weak contraction is introduced, which utilized to prove some fixed point results. These results are helpful give a positive response certain open question raised by Kannan and Rhoades on existence contractive definition does not force mapping be continuous at point. Some illustrative examples also given support our As applications result, we investigate uniquenes...

in this paper, we unify, extend and generalize some results on coupled fixed point theorems of generalized φ- mappings with some applications to fixed points of integral type mappings in cone metric spaces.

in the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.

In this paper, we extend the idea of α-ψ contraction mapping to product spaces by introducing Prešić–Ćirić-type contractions and utilize them prove some coincidence common fixed-point theorems in context ordered metric using α-admissibility mapping. Our newly established results generalize a number well-known from literature. Moreover, give examples that attest credibility our results. Further,...

This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: { D t x(t) = f(t, x(t), D β t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = ∫ 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle. Keywords—Fractional differential equation; Integral boundary condi...

In this study, we introduce a new definition called δ-contraction. However, prove some theorems for mappings satisfying the δ-contraction and touch upon fixed points. obtained theorems, also show existence uniqueness of order to validity results our main give few examples as well an application that reveals solution integral equations.

In this paper, we consider an inverse problem for three dimensional viscoelastic fluid flow equations, which arises from the motion of Kelvin-Voigt fluids in bounded domains (a hyperbolic type problem). This aims to reconstruct velocity and kernel memory term simultaneously, measurement described as integral over determination condition. By using contraction mapping principle appropriate space,...