A universal period doubling cascade analogous to the famous FeigenbaumCoullet-Tresser period doubling has been observed in area-preserving maps of R. Existence of the “universal” map with orbits of all binary periods has been proved via a renormalization approach in (Eckmann et al 1984) and (Gaidashev et al 2011). These proofs use “hard” computer assistance. In this paper we attempt to reduce c...

‎inspired by the work of suzuki in‎ ‎[t. suzuki‎, ‎a generalized banach contraction principle that characterizes metric completeness‎, proc‎. ‎amer‎. ‎math‎. ‎soc. ‎136 (2008)‎, ‎1861--1869]‎, ‎we prove a fixed point theorem for contractive mappings‎ ‎that generalizes a theorem of geraghty in [m.a‎. ‎geraghty‎, ‎on contractive mappings‎, ‎proc‎. ‎amer‎. ‎math‎. ‎soc., ‎40 (1973)‎, ‎604--608]‎an...

for all x, y ∈ X. Kannan [] proved that if X is complete, then a Kannan mapping has a fixed point. It is interesting that Kannan’s theorem is independent of the Banach contraction principle []. Also, Kannan’s fixed point theorem is very important because Subrahmanyam [] proved that Kannan’s theorem characterizes the metric completeness. That is, a metric space X is complete if and only if ev...

The famous Banach contraction principle (see, e.g., [1]) plays an important role in various fields of nonlinear analysis and applied mathematical analysis. Many authors investigated and established generalizations in various different directions of the Banach contraction principle in the past; see [1-22] and references therein. In 1969, Nadler [2] first proved a set-valued generalized version o...

In this paper, we discuss and extend some recent common fixed point results established by using $varphi-$weakly contractive mappings. A very important step in the development of the fixed point theory was given by A.H. Ansari by the introduction of a $C-$class function. Using $C-$class functions, we generalize some known fixed point results. This type of functions is a very important class of ...

In this paper, a coupled system of differential equations involving fractional order with integral boundary conditions is discussed. the problem at hand, three main aspects that are existence, uniqueness, and stability have been investigated. Firstly, contraction mapping principle used to discuss uniqueness solutions for proposed system, secondly, existence investigated based on Leray–Schauder’...

This paper studies a fractional boundary value problem of nonlinear differential equations of arbitrary orders. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. In order to clarify our results, some illustrative examples are also presented.