Fixed point and common fixed point results in cone metric space and application to invariant approximation

Abstract

In this work, the concept of almost contraction for multi-valued mappings in the setting of cone metric spaces is defined and then we establish some fixed point and common fixed point results in the set-up of cone metric spaces. As an application, some invariant approximation results are obtained. The results of this paper extend and improve the corresponding results of multi-valued mapping from metric space theory to cone metric spaces. Further our results improve the recent result of Arshad and Ahmad (Sci. World J. 2013:481601, 2013. MSC: 46T99; 47H10; 54H25

Common fixed point theorems in C∗ -algebra-valued metric spaces

“…The Banach contraction principle which shows that every contractive mapping has a unique fixed point in a complete metric space has been extended in many directions ( [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][18][19][20][21][22]). One of the branches of this theory is devoted to the study of common fixed points.…”

Some Novel Generalized Strong Coupled Fixed Point Findings in Cone Metric Spaces with Application to Integral Equations

“…Definition 1 (see [18]). A subset P of a real Banach space E is called a cone if (i) P ≠ ∅, closed, and P ≠ fθg, where θ is the zero elements of E…”

“…After the publication of this article, many researchers, i.e., Abbas and Jungck [9], Ilić and Rakočević [10], and P. Vetro [11] generalize their results for the FP, common FP, and coincidence points in CMS by using the contraction conditions. Some other related results can be found in (see [12][13][14][15][16][17][18][19][20][21][22][23] and the references are therein).…”

Common fixed point theorems in $C^*$-algebra-valued metric spaces

“…The Banach contraction principle, which shows that every contractive mapping has a unique fixed point in a complete metric space, has been extended in many directions ( [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][17][18][19][20][21][22]). One of the branches of this theory is devoted to the study of common fixed points.…”