Common best proximity points results for new proximal C-contraction mappings

Abstract

We define a new version of proximal C-contraction and prove the existence and uniqueness of a common best proximity point for a pair of non-self functions. Then we apply our main results to get some fixed point theorems and we give an example to illustrate our results.MSC: Primary 90C26; 90C30; secondary 47H09; 47H10

C-class functions and pair (F,h) Upper class on common best proximity points results for new proximal C-contraction mappings

“…[ [21]] to obtain some new common best proximity point theorems. Next, by an example and some fixed point results, we support our main result.…”

Existence of common best proximity point for single and multivalued non-self mappings

“…Suppose we have two non-self mappings f, g : A → B, the equations f x = x and gx = x are likely to have no common solution, known as common fixed point of the mappings f and g. In this situation, one wants to find approximate solution x such that the errors d(x, f x) and d(x, gx) are minimum for these two fixed point equations, called as common best proximity point of the mappings f and g. For detailed analysis on common best proximity point, we direct the reader to see [5,11,13,14,15,17,19].…”

Proximally Compatible Mappings and Common Best Proximity Points

“…Parvaneh Lo lo et al[13] proved a result which gives sufficient condition to exist a common best proximity point for four different mappings in metric-type spaces. One can get some ideas on results of common best proximity point for several kinds of non-self mappings which are available in [14][15][16][17][18] In this research paper, we provide the concept of proximally compatible mappings and we give common best proximity point theorems for proximally compatible non-self mappings. First, we prove some basic results from Jungck [1], which are analogous of self mappings.…”