Fixed point theorems on b-metric spaces for weak contractions with auxiliary functions

Abstract

In this paper, we obtain some fixed point results for generalized weakly contractive mappings with some auxiliary functions in the framework of b-metric spaces. The proved results generalize and extend the corresponding well-known results of the literature. Some examples are also provided in order to show that these results are more general than the well-known results existing in literature. MSC: Primary 47H10; secondary 54H25

Resolving systems of nonlinear integral equations via C-class functions

“…In Czerwik (1993) and Czerwik (1998) extended many results related to the bmetric spaces. Since then, several papers have been published on the fixed point theory of various classes of single-valued and multi-valued operators in b-metric spaces (Akkouchi, 2011;Aydi et al, 2012;Boriceanu, 2009;Boriceanu et al, 2010;Bota et al, 2011;Hussain & Shah, 2011;Olatinwo, 2008;Huang et al, 2015;Mustafa et al, 2013;Mustafa et al, 2014;Ansari et al, 2014;Aghajani et al, 2014).…”

“…Definition 1.6. (Ansari et al, 2014) . Therefore, in this paper we gives Theorem 1.11 which represents the continuation of Theorem 15 from Hussain et al (2014) on b-metric spaces whit the implementation of the functions of the C-class.…”

Fixed point theorems for ( F,\psi ,\varphi )-contractions on ordered S-Complete Hausdorff uniform spaces

“…In 2014, the concept of C-class functions were introduced by H. Ansari in [6]. After some fixed point theorems were gived using this concept ( [7], [12], [14]). …”

Some approximate fixed point results and application on graph theory for partial (h-F)-generalized convex contraction mappings with special class of functions on complete metric space

“…We say that T is an α-admissible mapping, if for all x, y ∈ X, α(x, y) 1 implies α(T x, T y) 1. 2,16]). Let T : X → X, ξ : X × X → R + .…”