Some Results on Fixed Points for Monotone Inward Mappings in Geodesic Spaces

في هذه الدراسة:تم انشاء متتابعة رتيبة في مجال دالة كارتسي الرتيبة المتجهة الى الداخل باستخدام الخاصية البينية التي تتمتع بها الفضاءات المترية الجيوديسية واثبات ان هذه المتتابعة تقترب الى النقطة الصامدة لتلك الدالة باستخدام نظرية كارتسي للنقطة الصامدة.In this article, the partially ordered relation is constructed in geodesic spaces by betweeness property, A monotone sequence is generated in the domain of monotone inward mapping,  a monotone inward contraction mapping is a  monotone Caristi inward mapping is proved, the general fixed points for such mapping is discussed and A mutlivalued version of these results is also introduced

Some Coupled coincidence and common fixed point theorems for hybrid pair of mappings

In this paper we extend the multi-valued mappings and obtain coupled coincidence points and common coupled fixed point theorems involving hybrid pair of single valued and multi-valued maps satisfying generalized contractive conditions in the frame work of a complete metric space. Keywords: coupled common fixed point, coupled coincidence point, coupled point of coincidence, w-compatible mappings, F-weakly commuting mappings

Contraction Mappings and Applications

The aim of the chapter is to find the existence results for the solution of non-homogeneous Fredholm integral equations of the second kind and non-linear matrix equations by using the fixed point theorems. Here, we derive fixed point theorems for two different type of contractions. Firstly, we utilize the concept of manageable functions to define multivalued α∗−η∗ manageable contractions and prove fixed point theorems for such contractions. After that, we use these fixed point results to find the solution of non-homogeneous Fredholm integral equations of the second kind. Secondly, we introduce weak F contractions named as α-F-weak-contraction to prove fixed point results in the setting of metric spaces and by using these results we find the solution for non-linear matrix equations

Using implicit relation to prove common coupled fixed point theorems for two hybrid pairs of mappings

Using implicit relation we establish two common coupled fixed point theorems under the conditions of weakly commutativity and w−compatibility on a complete metric space, which is not partially ordered. We do not use the condition of continuity of any mapping for proving the existence of coupled coincidence and common coupled fixed point.Publisher's Versio

Coupled fixed point theorems in complete metric spaces endowed with a directed graph and application

The purpose of this paper is to present some existence results for coupled fixed point of a .'; / contractive condition for mixed monotone operators in metric spaces endowed with a directed graph. Our results generalize the results obtained by Jain et al. in (International Journal of Analysis, Volume 2014, Article ID 586096, 9 pages). Moreover, we have an application to some integral system to support the result