The Meir-Keeler contraction, an important generalization of the classical Banach contraction has received enormous attention during the last four decades. In this paper, we present a review of Meir-Keeler type fixed point theorems and obtain some results using general Meir-Keeler type conditions for a sequence of maps in a metric space. Further, a recent result of Meir-Keeler type common fixed ...

We establish new fixed-point results involving implicit contractions on a metric space endowed with two metrics. The main results in this paper extend and generalize several existing fixed-point theorems in the literature.

Results on common fixed points for pairs of single and multivalued mappings on a complete metric space are examined. Our work establishes a common fixed point theorem for a pair of generalized contraction self-maps and a pair of set-valued mappings.

In this paper, by virtue of some analysis techniques, we prove a new common fixed point theorem of Altman type for four mappings satisfying a contractive condition of integral type in complete metric spaces, which improves and extends several previous results obtained by others.

*Correspondence: [email protected] 3Faculty of Mathematics and Computational Science, Xiangtan University, Hunan, 411105, P.R. China 4Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract In this paper, by applying ...

The purpose of this short paper is to study a simple differential equation of the advantage type, see Eq. (1). Such equations appear in several branches of applied mathematics, for example, see [ 1 ] for an application in probability. In this paper and for the simple type of equation considered, we show existence of a solution on any interval [0, T], where T is any positive finite constant, and...

In this paper, we establish sufficient conditions for the existence and nonexistence of positive solutions to the following nonlinear fractional differential system ⎪⎪⎨ ⎪⎪⎩ Dαu(t)+a(t) f (t,u,v) = 0 in (0,1) , Dβ v(t)+b(t)g(t,u,v) = 0 in (0,1) , u(0) = 0, u(1) = 0, u′(0) = 0, v(0) = 0, v(1) = 0, v′(0) = 0, (P) where 2 < α ,β 3 , a,b ∈ C ((0,1) , [0,+∞)) and the functions f ,g belong to C ([0,1]...

We have investigated the existence and uniqueness solutions of the nonlinear fractional differential equation of an arbitrary order with integral boundary condition. The result is an application of the Schauder fixed point theorem and the Banach contraction principle.

Let X be a Banach space, K a non-empty closed subset of X and let T : K → X be a non-self almost contraction. The main result of this paper shows that if T has the so called property (M) and satisfies Rothe’s boundary condition, i.e., maps ∂K (the boundary of K) into K, then T has a fixed point in K. This theorem generalizes several fixed point theorems for non-self mappings and also extends se...

In this paper we have considered the question of the existence of the solution of a pair of coupled ordinary differential equations depending on a parameters. By using a corollary of the SchauderTychonoff fixed point theorem, and some hard analysis needed to cover essentially the range of s near s=O we were able to show that all the conditions for the theorem could be fulfilled. Hence existence...