Common fixed points of mappings satisfying implicit contractive conditions

Abstract

In this article we obtain, in the setting of metric spaces or ordered metric spaces, coincidence point, and common fixed point theorems for self-mappings in a general class of contractions defined by an implicit relation. Our results unify, extend, generalize many related common fixed point theorems from the literature. Mathematics Subject Classification (2000): 47H10, 54H25.

Fixed points for Geraghty-Contractions in partial metric spaces

“…Indeed, many authors presented significant contributions in the directions of establishing partial metric versions of well-known fixed point theorems in classical metric spaces (see for example [8,12,14,43]). Obviously, we cannot cite all these papers but we give only a partial list [1]- [7], [11,13,15,16], [20]- [24], [32,33,36,37,44].…”

Common fixed points via implicit contractions on b-metric-like spaces

“…This direction was the source of several (common) fixed point and coincidence point theorems in various ambient spaces. For more details, see [5,[10][11][12]20]. Now, take s 1 and denote by N the set of positive integers.…”

Common Coupled Fixed Point Theorems for Two Hybrid Pairs of Mappings Satisfying an Implicit Relation

“…Fixed point theorems satisfying an implicit relation for single-valued and multivalued mappings under different conditions have been studied by various authors including ( [4], [5], [7], [9], [19], [24], [26], [27], [31], [33], [34], [35], [38]). …”