Existence of best proximity points satisfying two constraint inequalities

In this paper, we prove the existence of best proximity point and coupled best proximity point on metric spaces with partial order for weak proximal contraction mappings such that these critical points satisfy some constraint inequalities.

Optimal solutions and applications to nonlinear matrix and integral equations via simulation function

Based on the concepts of ?-proximal admissible mappings and simulation function, we establish some best proximity point and coupled best proximity point results in the context of b-complete b-metric spaces. We also provide some concrete examples to illustrate the obtained results. Moreover, we prove the existence of the solution of nonlinear integral equation and positive definite solution of nonlinear matrix equation X = Q + ?m,i=1 A*i?(X)Ai-?m,i=1 B*i(X)Bi. The given results not only unify but also generalize a number of existing results on the topic in the corresponding literature.

Some Random Coupled Best Proximity Points for a Generalized ω-Cyclic Contraction in Polish Spaces

In this paper, we will introduce the concepts of a random coupled best proximity point and then we prove the existence of random coupled best proximity points in separable metric spaces. Our results extend the previous work of Akbar et al.[1].

The Existence and Uniqueness of Coupled Best Proximity Point for Proximally Coupled Contraction in a Complete Ordered Metric Space

We prove the existence and uniqueness of coupled best proximity point for mappings satisfying the proximally coupled contraction in a complete ordered metric space. Further, our result provides an extension of a result due to Bhaskar and Lakshmikantham.