Abstract
In this paper, we introduce a new concept of random α -proximal admissible and random α - Z -contraction. Then we establish random best proximity point theorems for such mapping in complete separable metric spaces.
Highlights
Some well known random fixed point theorems are generalizations of classical fixed point theorems
In 2017, Karapinar and Khojasted [28] proved the existence of best proximity point theorems of certain mapping via simulation function of complete metric space
The purpose of this paper is to present some random best proximity point theorems for certain mapping via simulation functions in separable metric space
Summary
Some well known random fixed point theorems are generalizations of classical fixed point theorems. Random fixed point theorems for contraction mapping in a Polish space, i.e., a separable complete metric space, were proved by Špaček [1], Hanš [2,3]. In 2012, Samet et al [17] introduced a new class of α-ψ-contractive type mapping and establish fixed point theorems for such mapping in complete metric spaces. Introduced a new class of α-ψ-contractive type mapping to the case of non-selfmapping and establish best proximity point theorems for such mapping in complete metric spaces. In 2017, Karapinar and Khojasted [28] proved the existence of best proximity point theorems of certain mapping via simulation function of complete metric space. The purpose of this paper is to present some random best proximity point theorems for certain mapping via simulation functions in separable metric space
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