Random Common Fixed Point Theorem for Random Weakly Subsequentially Continuous Generalized Contractions With Application

Abstract

In this paper, we prove random common fixed point theorem for two pairs of random self mappings under a generalized contractive condition using subsequential continuity with compatibility of type (E). An example is given to justify our theorem. Our results in randomness extend and improve the results of S. Beloul [4]. Finally, we give an application to discuss the existence of a solution of random Hammerstein integral equations.

Random Common Fixed Point Theorems for Two Pairs of Nonlinear Contractive Maps in Polish Spaces

“…Remark : Theorem 2.1 gives an independent version of the result of Rashwan and Hammed [9](Theorem 9) because the result is proved without the assumption of weakly random subsequential continuity and compatibility of type (E). Theorem 2.1 proves the random version of the result of Eke and Akinlabi [8] (Theorem 2.1) with general contractive mappings in the context of Polish space.…”

“…The following theorems are the results of Eke and Akinlabi [8] and Rashwan and Hammed [9] respectively.…”

“…The common fixed point of two pairs of weakly compatible mappings satisfying certain contractive conditions in G-partial metric spaces without assuming the continuity of any of the maps involved was proved by Eke and Akinlabi [8]. The random common fixed point of two pairs of random subsequentially continuous mappings with compatibility of type (E) satisfying certain generalized contractive conditions in Polish spaces ( separable metric space) was established by Rashwan and Hammed [9]. In this paper, we prove the random version of the result of Eke and Akinlabi [8] in the context of Polish spaces by using the contractive maps of Rashwan and Hammed [9].…”

“…The random common fixed point of two pairs of random subsequentially continuous mappings with compatibility of type (E) satisfying certain generalized contractive conditions in Polish spaces ( separable metric space) was established by Rashwan and Hammed [9]. In this paper, we prove the random version of the result of Eke and Akinlabi [8] in the context of Polish spaces by using the contractive maps of Rashwan and Hammed [9]. Our results are extension and an improvement on some related results in the literature.…”

Random Fixed Point Theorem for Weakly Compatible Mappings under Implicit Relation in Cone Random Metric Spaces

“…The results ofŠpaček and Hanš in multi-valued contractive mappings was extended by Itoh [14]. Now this theory has become the full fledged research area and various ideas associated with random fixed point theory are used to give the solution of nonlinear system see [5-7, 11, 25] and nonlinear integral equation see [19][20][21]. Common random fixed points and random coincidence points of a pair of compatible random operators and fixed point theorems for contractive random operators in Polish spaces are obtained by Papageorgiou [17,18] and Beg [3,4].…”