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A class of generalized (ψ , α , β) —weak contraction is introduced and some fixed-point theorems in a framework of partially ordered metric spaces are proved. The main result of this paper is applied to a first-order ordinary differential equation to find its solution. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this work, we introduced new notions of a new contraction named S -weakly contraction; after that, we obtained the p-common best proximity point results for different types of contractions in the setting of complete metric spaces by using weak P p -property and proved the uniqueness of these points. Also, we presented some examples to prove the validity of our results. [ABSTRACT FROM AUTHOR]