Related Results to Hybrid Pair of Mappings and Applications in Bipolar Metric Spaces

In this paper, we introduce the concept of multivalued contraction mappings in partially ordered bipolar metric spaces and establish the existence of unique coupled fixed point results for multivalued contractive mapping by using mixed monotone property in partially ordered bipolar metric spaces. Some interesting consequences of our results are obtained.

BOX DIMENSION OF A NONLINEAR FRACTAL INTERPOLATION CURVE

In this paper, we present a delightful method to estimate the lower and upper box dimensions of a special nonlinear fractal interpolation curve. We use Rakotch contractibility and monotone property of function in the estimation of upper box dimension, and we use Rakotch contractibility, noncollinearity of interpolation points, nondecreasing property of function, convex (or concave) property of function and differential mean value theorem in the estimation of lower box dimension. In particular, we propose a well-founded conjecture motivated by our results.