We introduce the notion of α -admissibility of mappings on cone b-metric spaces using Banach algebra with coefficient s, and establish a result of the Hardy-Rogers theorem in these spaces. Furthermore, using symmetry, we derive many recent results as corollaries. As an application we prove certain fixed point results in partially ordered cone b-metric space using Banach algebra. Also, we use our results to derive and prove some real world problems to show the usability of our obtained results. Moreover, it is worth noticing that fixed point theorems for monotone operators in partially ordered metric spaces are widely investigated and have found various applications in differential, integral and matrix equations.
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.
Common coupled fixed point theorems for generalized T-contractions are proved for a pair of mappings S:X×X→X and g:X→X in a bv(s)-metric space, which generalize, extend, and improve some recent results on coupled fixed points. As an application, we prove an existence and uniqueness theorem for the solution of a system of nonlinear integral equations under some weaker conditions and given a convergence criteria for the unique solution, which has been properly verified by using suitable example.
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