The aim of this paper is to establish some common fixed point theorems under occasionally weakly compatible maps using implicit functions.

We present a new proof of the version of the Shauder-Tychonov theorem provided by Coppel in Stability and Asymptotic Behavior of Differential Equations, Heath Mathematical Monographs, Boston (1965). Our alternative proof mainly relies on the Schauder fixed point theorem.

*Correspondence: [email protected] 1Department of Mathematics, 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 We first introduce the concept of b-metric-like space which generalizes the notions of partial metric space, metric-like space and b-metric space. Then we establish the existence and...

We use the fixed point alternative theorem to prove the stability of the set-valued function equation c(x)F (h(x)) = F (x). This result enable us to prove the stability of some set-valued functional equations.

*Correspondence: [email protected] Department of Mathematics and Statistics, Central South University, 932 Lushan South Road, Changsha, 410083, China †Equal contributors Abstract In this paper, we study a class of generalized fractional order three-point boundary value problems that involve fractional derivative defined in terms of weight and scale functions. Using several fixed point t...

Several new fixed point results for compact permissible self maps in extension type spaces are presented in this paper.

In this paper, we prove some common fixed point results for pair of rational type of contractive mappings in the setting of complex valued b-metric spaces. Our results extend, generalize and improve the corresponding results of A. K .Dubey’ [48]. Key word: Complex valued b-metric space; common fixed point; Rational expression type of contractive mappings.

A Smarandache multi-space is a union of n spaces A 1 , A 2 , · · · , A n with some additional conditions holding. Combining Smarandache multi-spaces with classical metric spaces, the conception of multi-metric space is introduced. Some characteristics of a multi-metric space are obtained and Banach's fixed-point theorem is generalized in this paper.

Some new related fixed point results for two pairs of mappings on two symmetric spaces are established.

In common fixed point results for two maps defined on a G−cone metric space, satisfying generalized contractive conditions are obtained. These results generalize, improve and unify several well known comparable results in the literature.