No abstract

We present the notion of orthogonal F -metric spaces and prove some fixed and periodic point theorems for orthogonal ⊥ Ω -contraction. We give a nontrivial example to prove the validity of our result. Finally, as application, we prove the existence and uniqueness of the solution of a nonlinear fractional differential equation.

We study the notions of weak partial b-metric space and weak partial Hausdorff b-metric space. Moreover, we intend to generalize Nadler's theorem in weak partial b-metric space by using weak partial Hausdorff b-metric spaces. A non-trivial example to show the validity of our result is given.Mathematics Subject Classification 2010: 55M20, 47H10

Brinde [Approximating fixed points of weak contractions using the Picard itration, Nonlinear Anal. Forum 9 (2004), 43-53] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost Θcontraction mappings and present some best proximity point results for this new class of mappings. As applications, best proximity point and fixed point results for weak single valued Θ-contraction mappings are obtained. An example is presented to support the results presented herein. An application to a nonlinear differential equation is also provided.Mathematics Subject Classification 2010: 55M20, 47H10

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.