Common fixed point results for noncommuting mappings without continuity in cone metric spaces

Abstract

The existence of coincidence points and common fixed points for mappings satisfying certain contractive conditions, without appealing to continuity, in a cone metric space is established. These results generalize several well-known comparable results in the literature.

Some common random fixed point theorems for contractive type conditions in cone random metric spaces

“…Subsequently, several other authors [1,13,21,23] studied the existence of fixed points and common fixed points of mappings satisfying contractive type condition on a normal cone metric space.…”

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.…”

“…One such notion which is weaker than commuting is the concept of compatibility introduced by Jungck [13]. Subsequently, several authors have obtained coincidence and common fixed point results for mappings, utilizing this concept and its generalizations, see [1,4,7,11,14,19] and references therein.…”

Common fixed point under contractive condition of Ćirić’s type on cone metric type spaces

“…Cones and ordered normed spaces have some applications in optimization theory (see [5,6]). The initial study of Huang and Zhang [4] inspired many authors to prove fixed point theorems, as well as common fixed point theorems for two or more mappings on cone metric space, e.g., [7][8][9][10][11][12][13][14][15][16][17][18].…”